Stacks and Categories in Geometry, Topology, and Algebra

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American Mathematical Soc., 26 juin 2015 - 323 pages
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This volume contains the proceedings of the CATS4 Conference on Higher Categorical Structures and their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, held from July 2-7, 2012, at CIRM in Luminy, France.

Over the past several years, the CATS conference series has brought together top level researchers from around the world interested in relative and higher category theory and its applications to classical mathematical domains.

Included in this volume is a collection of articles covering the applications of categories and stacks to geometry, topology and algebra. Techniques such as localization, model categories, simplicial objects, sheaves of categories, mapping stacks, dg structures, hereditary categories, and derived stacks, are applied to give new insight on cluster algebra, Lagrangians, trace theories, loop spaces, structured surfaces, stability, ind-coherent complexes and 1-affineness showing up in geometric Langlands, branching out to many related topics along the way.

 

 

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Table des matières

Lagrangian structures on mapping stacks and semiclassical TFTs
1
Cluster categories for topologists
25
Crossed simplicial groups and structured surfaces
37
A model structure on relative dgLie algebroids
111
Multiple derived Lagrangian intersections
119
Sheaves of categories and the notion of 1affineness
127
Trace theories and localization
227
some remarks and conjectures
263
Indcoherent complexes on loop spaces and connections
289
Back Cover
325
Droits d'auteur

Expressions et termes fréquents

À propos de l'auteur (2015)

Tony Pantev, University of Pennsylvania, Philadelphia, PA, USA.

Carlos Simpson, Universite Nice Sophia Antipolis, France.

Bertrand Toen, Universite de Montpellier 2, France.

Michel Vaquie, Universite Paul Sabatier, Toulouse, France.

Gabriele Vezzosi, Universita degli Studi di Firenze, Italy.

Informations bibliographiques