Acta Mathematica

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• Mixing properties of commuting nilmanifold automorphisms AI翻译
  作者：Gorodnik, Alexander; Spatzier, Ralf
  作者单位：University of Bristol; University of Bristol; University of Michigan System; University of Michigan
  摘要：We study mixing properties of commutative groups of automorphisms acting on compact nilmanifolds. Assuming that every non-trivial element acts ergodically, we prove that such actions are mixing of all orders. We further show exponential 2-mixing and 3-mixing. As an application we prove smooth cocycle rigidity for higher-rank abelian groups of nilmanifold automorphisms.
• The convergence Newton polygon of a p-adic differential equation II: Continuity and finiteness on Berkovich curves AI翻译
  作者：Poineau, Jerome; Pulita, Andrea
  作者单位：Universite de Caen Normandie; Universite de Montpellier
  摘要：We study the variation of the convergence Newton polygon of a differential equation along a smooth Berkovich curve over a non-archimedean complete valued field of characteristic zero. Relying on work of the second author who investigated its properties on affinoid domains of the affine line, we prove that its slopes give rise to continuous functions that factorise by the retraction through a locally finite subgraph of the curve.
• On Vinogradov's mean value theorem: strongly diagonal behaviour via efficient congruencing AI翻译
  作者：Ford, Kevin; Wooley, Trevor D.
  作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Bristol
  摘要：We enhance the efficient congruencing method for estimating Vinogradov's integral for moments of order 2s, with . In this way, we prove the main conjecture for such even moments when , showing that the moments exhibit strongly diagonal behaviour in this range. There are improvements also for larger values of s, these finding application to the asymptotic formula in Waring's problem.
• Stable moduli spaces of high-dimensional manifolds AI翻译
  作者：Galatius, Soren; Randal-Williams, Oscar
  作者单位：Stanford University; University of Cambridge
  摘要：We prove an analogue of the Madsen-Weiss theorem for high-dimensional manifolds. In particular, we explicitly describe the ring of characteristic classes of smooth fibre bundles whose fibres are connected sums of g copies of S (n) xS (n) , in the limit . Rationally it is a polynomial ring in certain explicit generators, giving a high-dimensional analogue of Mumford's conjecture. More generally, we study a moduli space of those null-bordisms of a fixed (2n-1)-dimensional manifold P which are (n...
• Unique Cartan decomposition for II1 factors arising from arbitrary actions of free groups AI翻译
  作者：Popa, Sorin; Vaes, Stefaan
  作者单位：University of California System; University of California Los Angeles; KU Leuven
  摘要：We prove that for any free ergodic probability measure-preserving action of a free group on n generators , the associated group measure space II1 factor has L (a)(X) as its unique Cartan subalgebra, up to unitary conjugacy. We deduce that group measure space II1 factors arising from actions of free groups with different number of generators are never isomorphic. We actually prove unique Cartan decomposition results for II1 factors arising from arbitrary actions of a much larger family of group...
• Complete monotonicity for inverse powers of some combinatorially defined polynomials AI翻译
  作者：Scott, Alexander D.; Sokal, Alan D.
  作者单位：University of Oxford; New York University; University of London; University College London
  摘要：We prove the complete monotonicity on for suitable inverse powers of the spanning-tree polynomials of graphs and, more generally, of the basis generating polynomials of certain classes of matroids. This generalizes a result of SzegA and answers, among other things, a long-standing question of Lewy and Askey concerning the positivity of Taylor coefficients for certain rational functions. Our proofs are based on two ab-initio methods for proving that is completely monotone on a convex cone C: th...
• Every finite group is the group of self-homotopy equivalences of an elliptic space AI翻译
  作者：Costoya, Cristina; Viruel, Antonio
  作者单位：Universidad de Malaga; Universidade da Coruna; Universidad de Malaga
  摘要：We prove that every finite group G can be realized as the group of self-homotopy equivalences of infinitely many elliptic spaces X. To construct those spaces we introduce a new technique which leads, for example, to the existence of infinitely many inflexible manifolds. Further applications to representation theory will appear in a separate paper.
• Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton AI翻译
  作者：Martel, Yvan; Merle, Frank; Raphael, Pierre
  作者单位：Universite Paris Saclay; Institut Universitaire de France; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); CY Cergy Paris Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Universitaire de France
  摘要：We consider the quintic generalized Korteweg-de Vries equation (gKdV) which is a canonical mass critical problem, for initial data in H (1) close to the soliton. In earlier works on this problem, finite- or infinite-time blow up was proved for non-positive energy solutions, and the solitary wave was shown to be the universal blow-up profile, see [16], [26] and [20]. For well-localized initial data, finite-time blow up with an upper bound on blow-up rate was obtained in [18]. In this paper, we ...
• Geometric quantization for proper moment maps: the Vergne conjecture AI翻译
  作者：Ma, Xiaonan; Zhang, Weiping
  作者单位：Universite Paris Cite; Nankai University; Nankai University
  摘要：We establish an analytic interpretation for the index of certain transversally elliptic symbols on non-compact manifolds. By using this interpretation, we establish a geometric quantization formula for a Hamiltonian action of a compact Lie group acting on a non-compact symplectic manifold with proper moment map. In particular, we present a solution to a conjecture of MichSle Vergne in her ICM 2006 plenary lecture.
• K-homology and index theory on contact manifolds AI翻译
  作者：Baum, Paul F.; van Erp, Erik
  作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Dartmouth College
  摘要：This paper applies K-homology to solve the index problem for a class of hypoelliptic (but not elliptic) operators on contact manifolds. K-homology is the dual theory to K-theory. We explicitly calculate the K-cycle (i.e., the element in geometric K-homology) determined by any hypoelliptic Fredholm operator in the Heisenberg calculus. The index theorem of this paper precisely indicates how the analytic versus geometric K-homology setting provides an effective framework for extending formulas of...