Authors:Fedele; Francesca Pages: 342 - 373 Abstract: Let Φ be a finite-dimensional algebra over a field k. Kleiner described the Auslander–Reiten sequences in a precovering extension closed subcategory . If is an indecomposable such that and is the unique indecomposable direct summand of the -cover such that , then there is an Auslander–Reiten sequence in of the form Moreover, when modulo the morphisms factoring through a projective is a division ring, Kleiner proved that each non-split short exact sequence of the form is such that η is right almost split in , and the pushout of δ along g gives an Auslander–Reiten sequence in PubDate: 2020-01-15 DOI: 10.1017/S0013091519000312

Authors:Marcovecchio; Raffaele, Zudilin, Wadim Pages: 374 - 397 Abstract: We give a new hypergeometric construction of rational approximations to ζ(4), which absorbs the earlier one from 2003 based on Bailey's 9F8 hypergeometric integrals. With the novel ingredients we are able to gain better control of the arithmetic and produce a record irrationality measure for ζ(4). PubDate: 2020-02-03 DOI: 10.1017/S0013091519000427

Authors:Guo; Shaoming, Roos, Joris, Seeger, Andreas, Yung, Po-Lam Pages: 398 - 412 Abstract: Let M(u), H(u) be the maximal operator and Hilbert transform along the parabola (t, ut2). For U ⊂ (0, ∞) we consider Lp estimates for the maximal functions sup u∈U M(u)f and sup u∈U H(u)f , when 1 < p ≤ 2. The parabolas can be replaced by more general non-flat homogeneous curves. PubDate: 2020-02-03 DOI: 10.1017/S0013091519000439

Authors:Pacifico; M. J., Vieitez, J. L. Pages: 413 - 425 Abstract: We address the problem of defining Lyapunov exponents for an expansive homeomorphism f on a compact metric space (X, dist) using similar techniques as those developed in Barreira and Silva [Lyapunov exponents for continuous transformations and dimension theory, Discrete Contin. Dynam. Sys.13 (2005), 469–490]; Kifer [Characteristic exponents of dynamical systems in metric spaces, Ergod. Th. Dynam. Sys.3 (1983), 119–127]. Under certain conditions on the topology of the space X where f acts we obtain that there is a metric D defining the topology of X such that the Lyapunov exponents of f are different from zero with respect to D for every point x ∈ X. We give an example showing that this may not be true with respect to the original metric dist. But expansiveness of f ensures that Lyapunov exponents do not vanish on a Gδ subset of X with respect to any metric defining the topology of X. We define Lyapunov exponents on compact invariant sets of Peano spaces and prove that if the maximal exponent on the compact set is negative then the compact is an attractor. PubDate: 2020-02-10 DOI: 10.1017/S0013091519000579

Authors:Lewis; Mark L., Maglione, Joshua Pages: 426 - 442 Abstract: We enumerate the number of isoclinism classes of semi-extraspecial p-groups with derived subgroup of order p2. To do this, we enumerate GL (2, p)-orbits of sets of irreducible, monic polynomials in 'p[x]. Along the way, we also provide a new construction of an infinite family of semi-extraspecial groups as central quotients of Heisenberg groups over local algebras. PubDate: 2020-02-24 DOI: 10.1017/S0013091519000531

Authors:Elwes; Richard Pages: 443 - 455 Abstract: We consider a simple preferential attachment graph process, which begins with a finite graph and in which a new (t + 1)st vertex is added at each subsequent time step t that is connected to each previous vertex u ≤ t with probability du(t)/t, where du(t) is the degree of u at time t. We analyse the graph obtained as the infinite limit of this process, and we show that, as long as the initial finite graph is neither edgeless nor complete, with probability 1 the outcome will be a copy of the Rado graph augmented with a finite number of either isolated or universal vertices. PubDate: 2020-02-27 DOI: 10.1017/S0013091519000336

Authors:Bivià-Ausina; Carles, Ruas, Maria Aparecida Soares Pages: 456 - 474 Abstract: We extend the notions of μ*-sequences and Tjurina numbers of functions to the framework of Bruce–Roberts numbers, that is, to pairs formed by the germ at 0 of a complex analytic variety X ⊆ ℂn and a finitely -determined analytic function germ f : (ℂn, 0) → (ℂ, 0). We analyze some fundamental properties of these numbers. PubDate: 2020-02-27 DOI: 10.1017/S0013091519000543

Authors:Abrahamsen; T. A., Haller, R., Lima, V., Pirk, K. Pages: 475 - 496 Abstract: A Δ-point x of a Banach space is a norm-one element that is arbitrarily close to convex combinations of elements in the unit ball that are almost at distance 2 from x. If, in addition, every point in the unit ball is arbitrarily close to such convex combinations, x is a Daugavet point. A Banach space X has the Daugavet property if and only if every norm-one element is a Daugavet point. We show that Δ- and Daugavet points are the same in L1-spaces, in L1-preduals, as well as in a big class of Müntz spaces. We also provide an example of a Banach space where all points on the unit sphere are Δ-points, but none of them are Daugavet points. We also study the property that the unit ball is the closed convex hull of its Δ-points. This gives rise to a new diameter-two property that we call the convex diametral diameter-two property. We show that all C(K) spaces, K infinite compact Hausdorff, as well as all Müntz spaces have this property. Moreover, we show that this property is stable under absolute sums. PubDate: 2020-02-27 DOI: 10.1017/S0013091519000567

Authors:Vavilov; Nikolai, Zhang, Zuhong Pages: 497 - 511 Abstract: In the present paper, which is a direct sequel of our paper [14] joint with Roozbeh Hazrat, we prove an unrelativized version of the standard commutator formula in the setting of Chevalley groups. Namely, let Φ be a reduced irreducible root system of rank ≥ 2, let R be a commutative ring and let I,J be two ideals of R. We consider subgroups of the Chevalley group G(Φ, R) of type Φ over R. The unrelativized elementary subgroup E(Φ, I) of level I is generated (as a group) by the elementary unipotents xα(ξ), α ∈ Φ, ξ ∈ I, of level I. Obviously, in general, E(Φ, I) has no chance to be normal in E(Φ, R); its normal closure in the absolute elementary subgroup E(Φ, R) is denoted by E(Φ, R, I). The main results of [14] implied that the commutator [E(Φ, I), E(Φ, J)] is in fact normal in E(Φ, R). In the present paper we prove an unexpected result, that in fact [E(Φ, I), E(Φ, J)] = [E(Φ, R, I), E(Φ, R, J)]. It follows that the standard commutator formula also holds in the unrelativized form, namely [E(Φ, I), C(Φ, R, J)] = [E(Φ, I), E(Φ, J)], where C(Φ, R, I) is the full congruence subgroup of level I. In particular, E(Φ, I) is normal in C(Φ, R, I). PubDate: 2020-03-02 DOI: 10.1017/S0013091519000555

Authors:Biswas; Indranil, García-Prada, Oscar, Hurtubise, Jacques, Rayan, Steven Pages: 512 - 530 Abstract: For complex connected, reductive, affine, algebraic groups G, we give a Lie-theoretic characterization of the semistability of principal G-co-Higgs bundles on the complex projective line ℙ1 in terms of the simple roots of a Borel subgroup of G. We describe a stratification of the moduli space in terms of the Harder–Narasimhan type of the underlying bundle. PubDate: 2020-03-05 DOI: 10.1017/S0013091520000024

Authors:Poulain d'Andecy; L., Walker, R. Pages: 531 - 578 Abstract: We define and study cyclotomic quotients of affine Hecke algebras of type B. We establish an isomorphism between direct sums of blocks of these algebras and a generalization, for type B, of cyclotomic quiver Hecke algebras, which are a family of graded algebras closely related to algebras introduced by Varagnolo and Vasserot. Inspired by the work of Brundan and Kleshchev, we first give a family of isomorphisms for the corresponding result in type A which includes their original isomorphism. We then select a particular isomorphism from this family and use it to prove our result. PubDate: 2020-03-09 DOI: 10.1017/S0013091519000294

Authors:Hegenbarth; Friedrich, Repovš, Dušan Pages: 579 - 607 Abstract: The aim of this paper is to show the importance of the Steenrod construction of homology theories for the disassembly process in surgery on a generalized n-manifold Xn, in order to produce an element of generalized homology theory, which is basic for calculations. In particular, we show how to construct an element of the nth Steenrod homology group , where ?+ is the connected covering spectrum of the periodic surgery spectrum ?, avoiding the use of the geometric splitting procedure, the use of which is standard in surgery on topological manifolds. PubDate: 2020-03-20 DOI: 10.1017/S0013091520000012

Authors:Long; D. D., Reid, A. W. Pages: 305 - 313 Abstract: We give a new proof of a result of Sullivan [Hyperbolic geometry and homeomorphisms, in Geometric topology (ed. J. C. Cantrell), pp. 543–555 (Academic Press, New York, 1979)] establishing that all finite volume hyperbolic n-manifolds have a finite cover admitting a spin structure. In addition, in all dimensions greater than or equal to 5, we give the first examples of finite-volume hyperbolic n-manifolds that do not admit a spin structure. PubDate: 2019-12-05 DOI: 10.1017/S0013091519000324

Authors:Filipazzi; Stefano Pages: 314 - 322 Abstract: In this note, using methods introduced by Hacon et al. [‘Boundedness of varieties of log general type’, Proceedings of Symposia in Pure Mathematics, Volume 97 (American Mathematical Society, Providence, RI, 2018) 309–348], we study the accumulation points of volumes of varieties of log general type. First, we show that if the set of boundary coefficients Λ satisfies the descending chain condition (DCC), is closed under limits and contains 1, then the corresponding set of volumes satisfies the DCC and is closed under limits. Then, we consider the case of ε-log canonical varieties, for 0 < ε < 1. In this situation, we prove that if Λ is finite, then the corresponding set of volumes is discrete. PubDate: 2019-12-18 DOI: 10.1017/S0013091519000397 Issue No:Vol. 97 (2019)

Authors:Zare; Hadi Pages: 323 - 341 Abstract: This note is on spherical classes in when , with a special focus on the case of p=2 related to the Curtis conjecture. We apply Freudenthal's theorem to prove a vanishing result for the unstable Hurewicz image of elements in that factor through certain finite spectra. After either p-localization or p-completion, this immediately implies that elements of well-known infinite families in , such as Mahowaldean families, map trivially under the unstable Hurewicz homomorphism . We also observe that the image of the submodule of decomposable elements under the integral unstable Hurewicz homomorphism is given by . We apply the latter to completely determine spherical classes in for certain values of n>0 and d>0; this verifies Eccles' conjecture on spherical classes in , n>0, on finite loop spaces associated with spheres. PubDate: 2019-12-20 DOI: 10.1017/S0013091519000373