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作者：Khare, C; Ramakrishna, R
作者单位：Tata Institute of Fundamental Research (TIFR); Utah System of Higher Education; University of Utah; Cornell University
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作者：Przytycki, F; Rivera-Letelier, J; Smirnov, S
作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; State University of New York (SUNY) System; Stony Brook University; Royal Institute of Technology
摘要：We show equivalence of several standard conditions for non-uniform hyperbolicity of complex rational functions, including the Topological Collet-Eckmann condition (TCE), Uniform Hyperbolicity on Periodic orbits, Exponential Shrinking of components of pre-images of small discs, backward Collet-Eckmann condition at one point, positivity of the infimum of Lyapunov exponents of finite invariant measures on the Julia set. The condition TCE is stated in purely topological terms, so we conclude that ...
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作者：Mendelson, S; Vershynin, R
作者单位：Australian National University; University of Alberta
摘要：We solve Talagrand's entropy problem: the L-2-covering numbers of every uniformly bounded class of functions are exponential in its shattering dimension. This extends Dudley's theorem on classes of {0, 1}-valued functions, for which the shattering dimension is the Vapnik-Chervonenkis dimension. In convex geometry, the solution means that the entropy of a convex body K is controlled by the maximal dimension of a cube of a fixed side contained in the coordinate projections of K. This has a numbe...
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作者：Nakamura, G; Uhlmann, G
作者单位：Hokkaido University; University of Washington; University of Washington Seattle
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作者：Fomin, S; Zelevinsky, A
作者单位：University of Michigan System; University of Michigan; Northeastern University
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作者：Friedlander, EM; Walker, ME
作者单位：Northwestern University; University of Nebraska System; University of Nebraska Lincoln
摘要：The well known isomorphism relating the rational algebraic K-theory groups and the rational motivic cohomology groups of a smooth variety over a field of characteristic 0 is shown to be realized by a map (the Segre map) of infinite loop spaces. Moreover, the associated Chem character map on rational homotopy groups is shown to be a ring isomorphism. A technique is introduced that establishes a useful general criterion for a natural transformation of functors on quasi-projective complex varieti...
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作者：Graham, CR; Zworski, M
作者单位：University of Washington; University of Washington Seattle; University of California System; University of California Berkeley
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作者：Hausel, T; Thaddeus, M
作者单位：University of California System; University of California Berkeley; Columbia University
摘要：Among the major mathematical approaches to mirror symmetry are those of Batyrev-Borisov and Strominger-Yau-Zaslow (SYZ). The first is explicit and amenable to computation but is not clearly related to the physical motivation; the second is the opposite. Furthermore, it is far from obvious that mirror partners in one sense will also be mirror partners in the other. This paper concerns a class of examples that can be shown to satisfy the requirements of SYZ, but whose Hodge numbers are also equa...
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作者：Fu, BH
作者单位：Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper, firstly we calculate Picard groups of a nilpotent orbit O in a classical complex simple Lie algebra and discuss the properties of being Q-factorial and factorial for the normalization (O) over tilde of the closure of O. Then we consider the problem of symplectic resolutions for (O) over tilde. Our main theorem says that for any nilpotent orbit O in a semi-simple complex Lie algebra, equipped with the Kostant-Kirillov symplectic form omega, if for a resolution pi : Z --> (O) over...
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作者：Leary, IJ; Nucinkis, BEA
作者单位：University of Southampton; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：A group is of type VF if-it hag a finite-index subgroup which has a finite classifying space. We construct groups of type VF in which the centralizers of some elements of finite order are not of type VF and groups of type VF containing infinitely many conjugacy classes of finite subgroups. It follows that a group G of type VF need not admit a finite-type universal proper G-space. We construct groups G for which the minimal dimension of a universal proper G-space is strictly greater than the vi...
