Bigerbes and applications

Abstract: Gerbes are geometric objects on a space which represent degree 3 integer cohomology, in the same way that complex line bundles (classified by the Chern class) represent cohomology in degree 2. Among other settings, they arise naturally as obstructions to lifting the structure group of a principal G-bundle to a U(1) central extension of G. Higher versions of gerbes, representing cohomology classes of degree 4 and up, are typically complicated by higher categorical concepts (2-morphisms and so on) in their definition. In contrast, bigerbes (and their higher cousins) admit a simple, geometric, non-higher-categorical description, and provide a satisfactory account of the relationship between so-called `string structures' on a manifold and `fusion spin structures' on its loop space, among other applications. This is based on recent joint work with Richard Melrose.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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