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作者：Balogh, ZM; Buckley, SM
作者单位：University of Bern; Maynooth University
摘要：We prove the equivalence of three different geometric properties of metric-measure spaces with controlled geometry. The first property is the Gromov hyperbolicity of the quasihyperbolic metric. The second is a slice condition and the third is a combination of the Gehring-Hayman property and a separation condition.
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作者：Popa, M; Roth, M
作者单位：Harvard University; University of Michigan System; University of Michigan
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作者：Klartag, MB; Milman, VD
作者单位：Tel Aviv University
摘要：This paper proves that there exist 3n Steiner symmetrizations that transform any convex set K subset of R-n into an isomorphic Euclidean ball; i.e. if vol(K)=vol(D-n) where D-n is the standard Euclidean unit ball, then K can be transformed into a body (K) over tilde such that c(1)D(n) subset of (K) over tilde c(2)D(n), where c(1), c(2) are numerical constants. Moreover, for any c>2, cn symmetrizations are also enough.
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作者：Robinson, A
作者单位：University of Warwick
摘要：We prove that the stable homotopy of any Gamma-module F is the homology of a bicomplex Xi(F), in which the (q - 1)st row is the two-sided bar construction B(Lie(q)*, Sigma(q), F[q]). This gives a natural homotopical cotangent bicomplex for graded commutative algebras, in a form suitable for use in a new obstruction theory for classifying E-infinity ring structures on spectra. The E-infinity structure on certain Lubin-Tate spectra is a corollary.
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作者：Paternain, GP; Petean, J
作者单位：University of Cambridge; CIMAT - Centro de Investigacion en Matematicas
摘要：We show that if a closed manifold M admits an F-structure (not necessarily polarized, possibly of rank zero) then its minimal entropy vanishes. In particular, this is the case if M admits a non-trivial S-1 -action. As a corollary we obtain that the simplicial volume of a manifold admitting an F-structure is zero. We also show that if M admits an F-structure then it collapses with curvature bounded from below. This in turn implies that M collapses with bounded scalar curvature or, equivalently,...
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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...
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作者：Guan, PF; Ma, XN
作者单位：McMaster University; East China Normal University
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作者：Brunella, M
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Bourgogne Europe
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作者：Huybrechts, D
作者单位：Universite Paris Cite
