2017

最新文章

• Artin groups of Euclidean type AI翻译
  作者：McCammond, Jon; Sulway, Robert
  作者单位：University of California System; University of California Santa Barbara
  摘要：This article resolves several long-standing conjectures about Artin groups of Euclidean type. Specifically we prove that every irreducible Euclidean Artin group is a torsion-free centerless group with a decidable word problem and a finite-dimensional classifying space. We do this by showing that each of these groups is isomorphic to a subgroup of a group with an infinitet-ype Garside structure. The Garside groups involved are introduced here for the first time. They are constructed by applying...
• Links of rational singularities, L-spaces and LO fundamental groups AI翻译
  作者：Nemethi, Andras
  作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Eotvos Lorand University; Basque Center for Applied Mathematics (BCAM)
  摘要：We prove that the link of a complex normal surface singularity is an L-space if and only if the singularity is rational. This via a result of Hanselman et al. (Taut foliations on graph manifolds, 2015. arXiv: 1508.0591), proving the conjecture of Boyer et al. (Math Ann 356(4): 1213-1245, 2013), shows that a singularity link is not rational if and only if its fundamental group is left-orderable if and only if it admits a coorientable taut foliation.
• The boundary of an affine invariant submanifold AI翻译
  作者：Mirzakhani, Maryam; Wright, Alex
  作者单位：Stanford University
  摘要：We study the boundary of an affine invariant submanifold of a stratum of translation surfaces in a partial compactification consisting of all finite area Abelian differentials over nodal Riemann surfaces, modulo zero area components. The main result is a formula for the tangent space to the boundary. We also prove finiteness results concerning cylinders, a partial converse to the Cylinder Deformation Theorem, and a result generalizing part of the Veech dichotomy.
• The Fu-Yau equation with negative slope parameter AI翻译
  作者：Phong, Duong H.; Picard, Sebastien; Zhang, Xiangwen
  作者单位：Columbia University; University of California System; University of California Irvine
  摘要：The Fu-Yau equation is an equation introduced by Fu and Yau as a generalization to arbitrary dimensions of an ansatz for the Strominger system. As in the Strominger system, it depends on a slope parameter . The equation was solved in dimension 2 by Fu and Yau in two successive papers for , and for . In the present paper, we solve the Fu-Yau equation in arbitrary dimension for . To our knowledge, these are the first non-trivial solutions of the Fu-Yau equation in any dimension strictly greater ...
• Legendrian knots and constructible sheaves AI翻译
  作者：Shende, Vivek; Treumann, David; Zaslow, Eric
  作者单位：Boston College; University of California System; University of California Berkeley; Northwestern University
  摘要：We study the unwrapped Fukaya category of Lagrangian branes ending on a Legendrian knot. Our knots live at contact infinity in the cotangent bundle of a surface, the Fukaya category of which is equivalent to the category of constructible sheaves on the surface itself. Consequently, our category can be described as constructible sheaves with singular support controlled by the front projection of the knot. We use a theorem of Guillermou-Kashiwara-Schapira to show that the resulting category is i...
• Kodaira dimension of algebraic fiber spaces over abelian varieties AI翻译
  作者：Cao, Junyan; Pun, Mihai
  作者单位：Universite Paris Cite; Sorbonne Universite; Korea Institute for Advanced Study (KIAS)
  摘要：In this article we provide a proof of the Iitaka conjecture for algebraic fiber spaces over tori.
• Divisionally free arrangements of hyperplanes (vol 204, pg 317, 2016) AI翻译
  作者：Abe, Takuro
  作者单位：Kyushu University
• Wild ramification and spaces AI翻译
  作者：Achinger, Piotr
  作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Universite Paris Saclay
  摘要：We prove that every connected affine scheme of positive characteristic is a space for the ,tale topology. The main ingredient is the special case of the affine space over a field k. This is dealt with by induction on n, using a key Bertini-type statement regarding the wild ramification of -adic local systems on affine spaces, which might be of independent interest. Its proof uses in an essential way recent advances in higher ramification theory due to T. Saito. We also give rigid analytic and ...
• A fully nonlinear flow for two-convex hypersurfaces in Riemannian manifolds AI翻译
  作者：Brendle, Simon; Huisken, Gerhard
  作者单位：Columbia University; Eberhard Karls University of Tubingen
  摘要：We consider a one-parameter family of closed, embedded hypersurfaces moving with normal velocity , where denote the curvature eigenvalues and is a nonnegative constant. This defines a fully nonlinear parabolic equation, provided that . In contrast to mean curvature flow, this flow preserves the condition in a general ambient manifold. Our main goal in this paper is to extend the surgery algorithm of Huisken-Sinestrari to this fully nonlinear flow. This is the first construction of this kind fo...
• Norms on the cohomology of hyperbolic 3-manifolds AI翻译
  作者：Brock, Jeffrey F.; Dunfield, Nathan M.
  作者单位：Brown University; University of Illinois System; University of Illinois Urbana-Champaign
  摘要：We study the relationship between two norms on the first cohomology of a hyperbolic 3-manifold: the purely topological Thurston norm and the more geometric harmonic norm. Refining recent results of Bergeron, Aengun, and Venkatesh as well as older work of Kronheimer and Mrowka, we show that these norms are roughly proportional with explicit constants depending only on the volume and injectivity radius of the hyperbolic 3-manifold itself. Moreover, we give families of examples showing that some ...