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GEOMETRY AND TOPOLOGY (23 journals)

Showing 1 - 19 of 19 Journals sorted alphabetically
Annals of Global Analysis and Geometry     Hybrid Journal   (Followers: 1)
Applied General Topology     Open Access  
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry     Partially Free   (Followers: 1)
Computational Geometry     Hybrid Journal   (Followers: 3)
Computer Aided Geometric Design     Hybrid Journal   (Followers: 10)
Differential Geometry and its Applications     Full-text available via subscription   (Followers: 2)
Discrete & Computational Geometry     Hybrid Journal   (Followers: 6)
Geometriae Dedicata     Hybrid Journal   (Followers: 2)
Geometric and Functional Analysis : GAFA     Hybrid Journal   (Followers: 2)
Handbook of Differential Geometry     Full-text available via subscription  
Information Geometry     Hybrid Journal  
International Electronic Journal of Geometry     Open Access  
International Journal of Geometric Methods in Modern Physics     Hybrid Journal   (Followers: 2)
Journal of Applied and Computational Topology     Hybrid Journal  
Journal of Computational Geometry     Open Access   (Followers: 4)
Journal of Geometric Analysis     Hybrid Journal   (Followers: 2)
Journal of Geometry     Hybrid Journal   (Followers: 1)
Journal of Geometry and Physics     Full-text available via subscription  
Journal of Linear and Topological Algebra     Open Access   (Followers: 5)
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Journal of Geometry and Physics
Journal Prestige (SJR): 0.597
Citation Impact (citeScore): 1
Number of Followers: 0  
 
  Full-text available via subscription Subscription journal
ISSN (Print) 0393-0440 - ISSN (Online) 0393-0440
Published by Elsevier Homepage  [3306 journals]
  • Iteration of the exterior power on representation rings

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      Abstract: Publication date: July 2019Source: Journal of Geometry and Physics, Volume 141Author(s): Alain Connes In this note we investigate the idea of Michael Atiyah of using, as a possible approach to the Theorem of Feit–Thompson on the solvability of finite groups of odd order, the iterations of the transformation which replaces a representation of a finite group G on a finite dimensional complex vector space E by the difference between the associated representation of G on the sum of exterior powers of E and the trivial representation. We show that G has odd order if and only if the above operation extends to virtual representations and we then express it in terms of the exponential and the Adams operations in the complexified representation ring. We show the relevance of the idea in a concrete example by exhibiting convergence to a non-trivial character.
       
  • Harmonic forms and spinors on the Taub-bolt space

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      Abstract: Publication date: July 2019Source: Journal of Geometry and Physics, Volume 141Author(s): Guido Franchetti This paper studies the space of L2 harmonic forms and L2 harmonic spinors on Taub-bolt, a Ricci-flat Riemannian 4-manifold of ALF type. We prove that the space of harmonic square-integrable 2-forms on Taub-bolt is 2-dimensional and construct a basis. We explicitly find all L2 zero modes of D̸A, the Dirac operator twisted by an arbitrary L2 harmonic connection A, and independently compute the index of D̸A. We compare our results with those known in the case of Taub-NUT and Euclidean Schwarzschild as these manifolds present interesting similarities with Taub-bolt. In doing so, we generalise known results concerning harmonic spinors on Euclidean Schwarzschild.
       
  • D 4 +Drinfeld–Sokolov+hierarchy+and+quantum+singularity+theory&rft.title=Journal+of+Geometry+and+Physics&rft.issn=0393-0440&rft.date=&rft.volume=">Quantum D 4 Drinfeld–Sokolov hierarchy and quantum singularity theory

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      Abstract: Publication date: July 2019Source: Journal of Geometry and Physics, Volume 141Author(s): Ann du Crest de Villeneuve, Paolo Rossi In this paper we compute explicitly the double ramification hierarchy and its quantization for the D4 Dubrovin–Saito cohomological field theory obtained applying the Givental–Teleman reconstruction theorem to the D4 Coxeter group Frobenius manifold, or equivalently the D4 Fan–Jarvis–Ruan–Witten cohomological field theory (with respect to the non-maximal diagonal symmetry group J=Z∕3Z). We then prove its equivalence to the corresponding Dubrovin–Zhang hierarchy, which was known to coincide with the D4 Drinfeld–Sokolov hierarchy. Our techniques provide hence an explicit quantization of the D4 Drinfeld–Sokolov hierarchy. Moreover, since the DR hierarchy is well defined for partial CohFTs too, our approach immediately computes the DR hierarchies associated to the invariant sectors of the D4 CohFT with respect to folding of the Dynkin diagram, the B3 and G2 Drinfeld–Sokolov hierarchies.
       
  • Khovanov homology and binary dihedral representations for marked links

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      Abstract: Publication date: June 2019Source: Journal of Geometry and Physics, Volume 140Author(s): Sherry Gong We introduce a version of Khovanov homology for alternating links with marking data, ω, inspired by instanton theory. We show that the analogue of the spectral sequence from Khovanov homology to singular instanton homology introduced in Kronheimer and Mrowka (2011) for this marked Khovanov homology collapses on the E2 page for alternating links. We moreover show that for non-split links the Khovanov homology we introduce for alternating links does not depend on ω; thus, the instanton homology also does not depend on ω for non-split alternating links. Finally, we study a version of binary dihedral representations for links with markings, and show that for links of non-zero determinant, this also does not depend on ω.
       
  • Effective bounds for semistable sheaves on a threefold

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      Abstract: Publication date: June 2019Source: Journal of Geometry and Physics, Volume 140Author(s): Tohru Nakashima We give effective upper bounds for the third Chern characters and the dimensions of the cohomology groups of μ-semistable torsion-free sheaves on a smooth projective threefold. We also obtain bounds for the dimension of the moduli spaces of μ-stable vector bundles.
       
  • A class of homogeneous Finsler metrics

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      Abstract: Publication date: June 2019Source: Journal of Geometry and Physics, Volume 140Author(s): A. Tayebi, B. Najafi In this paper, we prove that every homogeneous (α,β)-metric is a stretch metric if and only if it is a Berwald metric. As its applications, we show that every R-quadratic or generalized Landsberg homogeneous (α,β)-metrics is Berwaldian.
       
  • String structures associated to indefinite Lie groups

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      Abstract: Publication date: June 2019Source: Journal of Geometry and Physics, Volume 140Author(s): Hisham Sati, Hyung-bo Shim String structures have played an important role in algebraic topology, via elliptic genera and elliptic cohomology, in differential geometry, via the study of higher geometric structures, and in physics, via partition functions. We extend the description of String structures from connected covers of the definite-signature orthogonal group O(n) to the indefinite-signature orthogonal group O(p,q), i.e. from the Riemannian to the pseudo-Riemannian setting. This requires that we work at the unstable level, which makes the discussion more subtle than the stable case. Similar, but much simpler, constructions hold for other noncompact Lie groups such as the unitary group U(p,q) and the symplectic group Sp(p,q). This extension provides a starting point for an abundance of constructions in (higher) geometry and applications in physics.
       
  • The geometry of generalized Cheeger–Gromoll metrics on the total space
           of transitive Euclidean Lie algebroids

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      Abstract: Publication date: June 2019Source: Journal of Geometry and Physics, Volume 140Author(s): Mohamed Boucetta, Hasna Essoufi Natural metrics (Sasaki metric, Cheeger–Gromoll metric, Kaluza–Klein metrics etc. ) on the tangent bundle of a Riemannian manifold is a central topic in Riemannian geometry. Generalized Cheeger–Gromoll metrics is a family hp,q of natural metrics on the tangent bundle depending on two parameters with p∈R and q≥0. This family possesses interesting geometric properties. If p=q=0 we recover the Sasaki metric and when p=q=1 we recover the classical Cheeger–Gromoll metric. A transitive Euclidean Lie algebroid is a transitive Lie algebroid with a Euclidean product on its total space. In this paper, we show that the analogous of natural metrics 1can be built in a natural way on the total space of transitive Euclidean Lie algebroids. Then we study the properties of generalized Cheeger–Gromoll metrics on this new context. We show a rigidity result of these metrics which generalizes some rigidity results known in the case of the tangent bundle. We show also that considering natural metrics on the total space of transitive Euclidean Lie algebroids opens new interesting horizons. For instance, Atiyah Lie algebroids constitute an important class of transitive Lie algebroids and we will show that natural metrics on the total space of Atiyah Euclidean Lie algebroids have interesting properties. In particular, if M is a Riemannian manifold of dimension n, then the Atiyah Lie algebroid associated to the O(n)-principal bundle of orthonormal frames over M possesses a family depending on a parameter k>0 of transitive Euclidean Lie algebroids structures say AO(M,k). When M is a space form of constant curvature c, we show that there exist two constants Cn0 such that (AO(M,k),h1,1) is a Riemannian manifold with positive scalar curvature if and only if c>Cn and 0
       
  • P n +and+an+ r -matrix+associated+with+the+universal+elliptic+curve&rft.title=Journal+of+Geometry+and+Physics&rft.issn=0393-0440&rft.date=&rft.volume=">Poisson structures on loop spaces of ℂ P n and an r -matrix
           associated with the universal elliptic curve

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      Abstract: Publication date: June 2019Source: Journal of Geometry and Physics, Volume 140Author(s): Alexander Odesskii We construct a family of Poisson structures of hydrodynamic type on the loop space of ℂPn−1. This family is parametrized by the moduli space of elliptic curves or, in other words, by the modular parameter τ. This family can be lifted to a homogeneous Poisson structure on the loop space of ℂn but in order to do that we need to upgrade the modular parameter τ to an additional field τ(x) with Poisson brackets {τ(x),τ(y)}=0,{τ(x),za(y)}=2πiza(y)δ′(x−y) where z1,…,zn are coordinates on ℂn. These homogeneous Poisson structures can be written in terms of an elliptic r-matrix of hydrodynamic type.
       
  • Taylor series and twisting-index invariants of coupled
           spin–oscillators

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      Abstract: Publication date: June 2019Source: Journal of Geometry and Physics, Volume 140Author(s): Jaume Alonso, Holger R. Dullin, Sonja Hohloch About six years ago, semitoric systems on 4-dimensional manifolds were classified by Pelayo & Vũ Ngọc by means of five invariants. A standard example of such a system is the coupled spin–oscillator on S2×R2. Calculations of three of the five semitoric invariants of this system (namely the number of focus–focus singularities, the generalised semitoric polygon, and the height invariant) already appeared in the literature, but the so-called twisting index was not yet computed and, of the so-called Taylor series invariant, only the linear terms were known.In the present paper, we complete the list of invariants for the coupled spin–oscillator by calculating higher order terms of the Taylor series invariant and by computing the twisting index. Moreover, we prove that the Taylor series invariant has certain symmetry properties that make the even powers in one of the variables vanish and allow us to show superintegrability of the coupled spin–oscillator on the zero energy level.
       
  • Primitive forms for Gepner singularities

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      Abstract: Publication date: June 2019Source: Journal of Geometry and Physics, Volume 140Author(s): Andrei Ionov We provide a construction of Saito primitive forms for Gepner singularity by studying the relation between Saito primitive forms for Gepner singularities and primitive forms for singularities of the form Fk,n=∑i=1nxik invariant under the natural Sn-action.
       
  • Sasaki–Einstein metrics on a class of 7-manifolds

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      Abstract: Publication date: June 2019Source: Journal of Geometry and Physics, Volume 140Author(s): Charles P. Boyer, Christina W. Tønnesen-Friedman In this note we give an explicit construction of Sasaki–Einstein metrics on a class of simply connected 7-manifolds with the rational cohomology of the 2-fold connected sum of S2×S5. The homotopy types are distinguished by torsion in H4.
       
  • Non-existence of certain type of convex functions on a Riemannian manifold
           with a pole

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      Abstract: Publication date: June 2019Source: Journal of Geometry and Physics, Volume 140Author(s): Absos Ali Shaikh, Chandan Kumar Mondal, Izhar Ahmad This paper is devoted to the study of non-existence of certain type of convex functions on a Riemannian manifold with a pole. To this end, we have developed the notion of odd and even functions on a Riemannian manifold with a pole and proved the non-existence of non-trivial and non-negative differentiable odd convex function whose gradient is complete. Finally, we have deduced an inequality related with convex function.
       
  • Riemann theta function solutions of the
           Caudrey–Dodd–Gibbon–Sawada–Kotera hierarchy

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      Abstract: Publication date: June 2019Source: Journal of Geometry and Physics, Volume 140Author(s): Xianguo Geng, Guoliang He, Lihua Wu The Caudrey–Dodd–Gibbon–Sawada–Kotera hierarchy associated with a 3 × 3 matrix spectral problem is proposed with the aid of Lenard recursion equations. By using the characteristic polynomial of Lax matrix for the Caudrey–Dodd–Gibbon–Sawada–Kotera hierarchy, we introduce a three-sheeted Riemann surface Km−1 of arithmetic genus m−1, from which we derive the associated Baker–Akhiezer function, the meromorphic function on it. Based on the theory of Riemann surfaces, we construct the explicit Riemann theta function representations of the Baker–Akhiezer function, the meromorphic function, and solutions for the Caudrey–Dodd–Gibbon–Sawada–Kotera hierarchy.
       
  • Planarity conditions and four-body central configurations equations with
           angles as coordinates

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      Abstract: Publication date: June 2019Source: Journal of Geometry and Physics, Volume 140Author(s): Manuele Santoprete We discuss several conditions for four points to lie on a plane, and we use them to find new equations for four-body central configurations that use angles as variables. We use these equations to give novel proofs of some results for four-body central configuration. We also give a clear geometrical explanation of why Ptolemy’s theorem can be used to write equations for co-circular central configurations when mutual distances are used as coordinates.
       
  • Elliptic equation with critical and negative exponents involving the GJMS
           operator on compact Riemannian manifolds

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      Abstract: Publication date: June 2019Source: Journal of Geometry and Physics, Volume 140Author(s): Mohammed Benalili, Ali Zouaoui In this paper we consider an elliptic equation with critical and negative exponents involving the GJMS (Graham–Jenne–Mason–Sparling) operator of order k on n-dimensional compact Riemannian manifolds with 2k
       
  • Gamma spaces and information

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      Abstract: Publication date: June 2019Source: Journal of Geometry and Physics, Volume 140Author(s): Matilde Marcolli We investigate the role of Segal’s Gamma-spaces in the context of classical and quantum information, based on categories of finite probabilities with stochastic maps and density matrices with quantum channels. The information loss functional extends to the setting of probabilistic Gamma-spaces considered here. The Segal construction of connective spectra from Gamma-spaces can be used in this setting to obtain spectra associated to certain categories of gapped systems.
       
  • Bi-Lagrangian structures on nilmanifolds

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      Abstract: Publication date: June 2019Source: Journal of Geometry and Physics, Volume 140Author(s): M.J.D. Hamilton We study bi-Lagrangian structures (a symplectic form with a pair of complementary Lagrangian foliations, also known as para-Kähler or Künneth structures) on nilmanifolds of dimension less than or equal to 6. In particular, building on previous work of several authors, we determine which 6-dimensional nilpotent Lie algebras admit a bi-Lagrangian structure. In dimension 6, there are (up to isomorphism) 26 nilpotent Lie algebras which admit a symplectic form, 16 of which admit a bi-Lagrangian structure and 10 of which do not. We also calculate the curvature of the canonical connection of these bi-Lagrangian structures.
       
  • Periodic motion in non-axially symmetric galaxies

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      Abstract: Publication date: June 2019Source: Journal of Geometry and Physics, Volume 140Author(s): Jaume Llibre, Claudio Vidal We apply the averaging theory for proving the existence of twelve families of periodic orbits in a three-dimensional galactic Hamiltonian system.
       
  • a 4 +for+non+minimal+Laplace+type+operators&rft.title=Journal+of+Geometry+and+Physics&rft.issn=0393-0440&rft.date=&rft.volume=">Heat coefficient a 4 for non minimal Laplace type operators

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      Abstract: Publication date: Available online 21 March 2019Source: Journal of Geometry and PhysicsAuthor(s): B. Iochum, T. Masson Given a smooth hermitean vector bundle V of fiber ℂN over a compact Riemannian manifold and ∇ a covariant derivative on V, let P=−( g −1∕2∇μ g 1∕2gμνu∇ν+pμ∇μ+q) be a non minimal Laplace type operator acting on smooth sections of V where u,pν,q are MN(ℂ)-valued functions with u positive and invertible. For any a∈Γ(End(V)), we consider the asymptotics Trae−tP∼t↓0∑r=0∞ar(a,P)t(r−d)∕2 where the coefficients ar(a,P) can be written as an integral of the functions ar(a,P)(x)=tr[a(x)ℛr(x)].This paper revisits the previous computation of ℛ2 by the authors and is mainly devoted to a computation of ℛ4. The results are presented with u-dependent operators which are universal (i.e
       
  • n -Hom-Lie+algebras&rft.title=Journal+of+Geometry+and+Physics&rft.issn=0393-0440&rft.date=&rft.volume=">Cohomologies, deformations and extensions of n -Hom-Lie algebras

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      Abstract: Publication date: Available online 19 March 2019Source: Journal of Geometry and PhysicsAuthor(s): Lina Song, Rong Tang In this paper, first we give the cohomologies of an n-Hom-Lie algebra and introduce the notion of a derivation of an n-Hom-Lie algebra. We show that a derivation of an n-Hom-Lie algebra is a 1-cocycle with the coefficient in the adjoint representation. We also give the formula of the dual representation of a representation of an n-Hom-Lie algebra. Then, we study (n−1)-order deformation of an n-Hom-Lie algebra. We introduce the notion of a Hom-Nijenhuis operator, which could generate a trivial (n−1)-order deformation of an n-Hom-Lie algebra. Finally, we introduce the notion of a generalized derivation of an n-Hom-Lie algebra, by which we can construct a new n-Hom-Lie algebra, which is called the generalized derivation extension of an n-Hom-Lie algebra.
       
  • Lightlike submanifolds of golden semi–Riemannian manifolds

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      Abstract: Publication date: Available online 15 March 2019Source: Journal of Geometry and PhysicsAuthor(s): Nergiz (Önen) Poyraz, Erol Yaşar We present lightlike submanifolds of golden semi–Riemannian manifolds. We prove that there is no radical anti–invariant lightlike submanifolds of a golden semi–Riemannian manifold. In particular, we investigate several properties of semi–invariant lightlike submanifolds of golden semi–Riemannian manifolds and we get some results. Moreover, we give two special examples.
       
  • S p ( n , 1 ) +'&rft.title=Journal+of+Geometry+and+Physics&rft.issn=0393-0440&rft.date=&rft.volume=">How to prove the Baum–Connes conjecture for the groups S p ( n , 1 )
           '

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      Abstract: Publication date: Available online 14 March 2019Source: Journal of Geometry and PhysicsAuthor(s): Pierre Julg We present a programme of proof of the Baum–Connes conjecture with coefficients for G=Sp(n,1) or F4(-20), i.e. simple Lie groups of real rank one having Kazhdan’s property (T). We use the geometry of the boundary sphere to produce a G-Fredholm module, together with a homotopy to the trivial representation through uniformly bounded representations. The strip of uniformly bounded representations of M. Cowling plays here the role of the complementary series. We explain how, modulo some conjectural estimates, this construction would prove the conjecture.
       
  • U ( 2 ) × U ( 3 ) +gauge+theory+extension+of+the+standard+model&rft.title=Journal+of+Geometry+and+Physics&rft.issn=0393-0440&rft.date=&rft.volume=">A U ( 2 ) × U ( 3 ) gauge theory extension of the standard model

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      Abstract: Publication date: Available online 14 March 2019Source: Journal of Geometry and PhysicsAuthor(s): Rafael Herrera, Alexander Quintero Vélez We consider an extension of the standard model based on the group U(2)×U(3), which is naturally compatible with the standard model interacting-particle representations and the spontaneous symmetry breaking of U(2)×U(3) to an electrostrong U(3). In its minimal version, the model only adds one extra U(1) gauge boson and it implies that the hypercharge is distributed between the factors of the hyperweak and hyperstrong forces. We show that the anomaly cancellation condition can be solved by adding exotic fermions associated with a 16-dimensional representation of U(2)×U(3). A brief discussion of the mechanism of the spontaneous breakdown of U(2)×U(3) in the gauge boson sector is given.
       
  • s o ( 3 ) +type+AKNS+hierarchies+as+well+as+a+gallery+of+simple+Lie+algebras+contained+in+ s l ( 3 ; ) &rft.title=Journal+of+Geometry+and+Physics&rft.issn=0393-0440&rft.date=&rft.volume=">The quasi-AKNS and quasi- s o ( 3 ) type AKNS hierarchies as well as a
           gallery of simple Lie algebras contained in s l ( 3 ; ℂ )

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      Abstract: Publication date: Available online 7 March 2019Source: Journal of Geometry and PhysicsAuthor(s): Hui Chang, Yuxia Li, Huanhe Dong, Hongyan Zhi This paper provides a new representation of sl(3;ℂ), i.e., a high-dimensional special linear Lie algebra A, which contributes to the generation of a series of simple Lie algebras owning different bases with inequable commutators. Their counterparts are obtained in succession by using some special invertible linear transformations. As applications, the quasi-AKNS and quasi-so(3) type AKNS Hamiltonian hierarchies as well as their nonlinear continuous integrable couplings with the Hamiltonian structures are established, respectively.
       
 
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