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作者：Fu, Baohua; Hwang, Jun-Muk
作者单位：Korea Institute for Advanced Study (KIAS); Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：The prolongation of a linear Lie algebra plays an important role in the study of symmetries of G-structures. Cartan and Kobayashi-Nagano have given a complete classification of irreducible linear Lie algebras with non-zero prolongations. If is the Lie algebra of infinitesimal linear automorphisms of a projective variety SaS,a(TM) V, its prolongation is related to the symmetries of cone structures, an important example of which is the variety of minimal rational tangents in the study of unirule...
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作者：Winter, Wilhelm
作者单位：University of Nottingham
摘要：In this article I study a number of topological and algebraic dimension type properties of simple C*-algebras and their interplay. In particular, a simple C*-algebra is defined to be (tracially) (m, m (m) over bar)-pure, if it has (strong tracial) m-comparison and is (tracially) (m) over bar -almost divisible. These notions are related to each other, and to nuclear dimension. The main result says that if a separable, simple, nonelementary, unital C*algebra with locally finite nuclear dimension...
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作者：Bartholdi, Laurent; Erschler, Anna
作者单位：University of Gottingen; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：We study the geometry of a class of group extensions, containing permutational wreath products, which we call permutational extensions. We construct for all k is an element of N a torsion group K-k with growth function upsilon K-k (n) similar to exp(n(1-(1-alpha)k)), 2(3-3/alpha) + 2(2-2/alpha) + 2(1-1/alpha) = 2, and a torsion-free group H-k with growth function upsilon H-k (n) similar to exp(log(n)n(1-(1-alpha)k)). These are the first examples of groups of intermediate growth for which the a...
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作者：Chen, Xuezhang; Xu, Xingwang
作者单位：National University of Singapore; Nanjing University; Nanjing University; Peking University
摘要：For the problem of finding a geometry on S-n, for n >= 3, with a prescribed scalar curvature, there is a well- known result which is called the perturbation theorem; it is due to Chang and Yang (Duke Math. J. 64, 27-69, 1991). Their key assumption is that the candidate f for the prescribed scalar curvature is sufficiently near the scalar curvature of the standard metric in the sup norm. It is important to know how large that difference in sup norm can possibly be. Here we consider prescribing ...
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作者：Ayoub, Joseph; Zucker, Steven
作者单位：University of Zurich; Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); Johns Hopkins University
摘要：We introduce the notion of Artin motives and cohomological motives over a scheme X. Given a cohomological motive M over X, we consider the universal Artin motive mapping to M and denote it omega(0)(X) ( M). We use this to define a motive E-X over X which is an invariant of the singularities of X. The first half of the paper is devoted to the study of the functors omega(0)(X) and the computation of the motives E-X.
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作者：Andersson, Mats; Samuelsson, Hakan
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：Let X be a complex space of pure dimension. We introduce fine sheaves of (0,q)-currents, which coincides with the sheaves of smooth forms on the regular part of X, so that the associated Dolbeault complex yields a resolution of the structure sheaf . Our construction is based on intrinsic and quite explicit semi-global Koppelman formulas.
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作者：Church, Thomas
作者单位：University of Chicago
摘要：Let C (n) (M) be the configuration space of n distinct ordered points in M. We prove that if M is any connected orientable manifold (closed or open), the homology groups H (i) (C (n) (M);ae) are representation stable in the sense of Church and Farb (arXiv:1008.1368). Applying this to the trivial representation, we obtain as a corollary that the unordered configuration space B (n) (M) satisfies classical homological stability: for each i, H (i) (B (n) (M); Q) approximate to H-i (B (n+1)(M); Q) ...
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作者：Guichard, Olivier; Wienhard, Anna
作者单位：Princeton University; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：The notion of Anosov representations has been introduced by Labourie in his study of the Hitchin component for SL(n,R). Subsequently, Anosov representations have been studied mainly for surface groups, in particular in the context of higher Teichmuller spaces, and for lattices in SO(1,n). In this article we extend the notion of Anosov representations to representations of arbitrary word hyperbolic groups and start the systematic study of their geometric properties. In particular, given an Anos...
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作者：Abouzaid, Mohammed
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We prove that the inclusion of every closed exact Lagrangian with vanishing Maslov class in a cotangent bundle is a homotopy equivalence. We start by adapting an idea of Fukaya-Seidel-Smith to prove that such a Lagrangian is equivalent to the zero section in the Fukaya category with integral coefficients. We then study an extension of the Fukaya category in which Lagrangians equipped with local systems of arbitrary dimension are admitted as objects, and prove that this extension is generated, ...
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作者：Ballard, Matthew; Favero, David; Katzarkov, Ludmil
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Vienna
摘要：The Orlov spectrum is a new invariant of a triangulated category. It was introduced by D. Orlov, building on work of A. Bondal-M. Van den Bergh and R. Rouquier. The supremum of the Orlov spectrum of a triangulated category is called the ultimate dimension. In this work, we study Orlov spectra of triangulated categories arising in mirror symmetry. We introduce the notion of gaps and outline their geometric significance. We provide the first large class of examples where the ultimate dimension i...
