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作者：Fukaya, Kenji; Seidel, Paul; Smith, Ivan
作者单位：Kyoto University; Massachusetts Institute of Technology (MIT); University of Cambridge
摘要：We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology. An essentially equivalent result was recently proved independently by Nadler [16], using a different...
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作者：Cautis, Sabin; Kamnitzer, Joel
作者单位：Rice University; University of California System; University of California Berkeley
摘要：Using derived categories of equivariant coherent sheaves we construct a knot homology theory which categorifies the quantum sl(m) knot polynomial. Our knot homology naturally satisfies the categorified MOY relations and is conjecturally isomorphic to Khovanov-Rozansky homology. Our construction is motivated by the geometric Satake correspondence and is related to Manolescu's by homological mirror symmetry.
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作者：Bartels, Arthur; Lueck, Wolfgang; Reich, Holger
作者单位：University of Munster; Heinrich Heine University Dusseldorf
摘要：We prove the K-theoretic Farrell-Jones conjecture for hyperbolic groups with (twisted) coefficients in any associative ring with unit.
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作者：Wenger, Stefan
作者单位：New York University
摘要：In this article we exhibit the largest constant in a quadratic isoperimetric inequality which ensures that a geodesic metric space is Gromov hyperbolic. As a particular consequence we obtain that Euclidean space is a borderline case for Gromov hyperbolicity in terms of the isoperimetric function. We prove similar results for the linear filling radius inequality. Our results strengthen and generalize theorems of Gromov, Papasoglu and others.
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作者：Caldero, Philippe; Keller, Bernhard
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Universite Paris Cite
摘要：The cluster category is a triangulated category introduced for its combinatorial similarities with cluster algebras. We prove that a cluster algebra A of finite type can be realized as a Hall algebra, called exceptional Hall algebra, of the cluster category. This realization provides a natural basis for A. We prove new results and formulate conjectures on ` good basis' properties, positivity, denominator theorems and toric degenerations.
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作者：Habiro, Kazuo
作者单位：Kyoto University
摘要：We construct an invariant J(M) of integral homology spheres M with values in a completion (Z[q]) over cap of the polynomial ring Z[ q] such that the evaluation at each root of unity. gives the the SU( 2) Witten-Reshetikhin-Turaev invariant tau(zeta) ( M) of M at. Thus zeta unifies all the SU( 2) Witten Reshetikhin -Turaev invariants of M. It also follows that tau(zeta) (M) as a function on. behaves like an analytic function defined on the set of roots of unity.
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作者：Riviere, Tristan
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：A new formulation for the Euler-Lagrange equation of the Willmore functional for immersed surfaces in R-m is given as a nonlinear elliptic equation in divergence form, with non-linearities comprising only Jacobians. Letting (H) over right arrow be the mean curvature vector of the surface, our new formulation reads L (H) over right arrow = 0, where L is a well-defined locally invertible self-adjoint elliptic operator. Several consequences are studied. In particular, the long standing open probl...
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作者：Papanikolas, Matthew A.
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：We develop a theory of Tannakian Galois groups for t-motives and relate this to the theory of Frobenius semilinear difference equations. We show that the transcendence degree of the period matrix associated to a given t-motive is equal to the dimension of its Galois group. Using this result we prove that Carlitz logarithms of algebraic functions that are linearly independent over the rational function field are algebraically independent.
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作者：Cluckers, Raf; Loeser, Francois
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); KU Leuven
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作者：Peyre, Emmanuel
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Centre National de la Recherche Scientifique (CNRS)
摘要：Let G be a finite group and W be a faithful representation of G over C. The group G acts on the field of rational functions C(W). The question whether the field of invariant functions C(W)(G) is purely transcendental over C goes back to Emmy Noether. Using the unramified cohomology group of degree 2 of this field as an invariant, Saltman gave the first examples for which C(W)(G) is not rational over C. Around 1986, Bogomolov gave a formula which expresses this cohomology group in terms of the ...
