TQFT’s and gerbes

2003/02/28 by Roger Picken
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Abelian group #Black Holes and Theoretical Physics #Combinatorics #Connection (principal bundle) #Field (mathematics) #Geometry #Mathematical physics #Mathematics #Microtubule and mitosis dynamics #Noncommutative and Quantum Gravity Theories #Pure mathematics #Quantum field theory #Topological quantum field theory #Topology (electrical circuits) #math.DG #msc:53C29 #msc:55R65

paper · pdf · doi:10.2140/agt.2004.4.243

published as Algebr. Geom. Topol. 4 (2004) 243-272 · Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-14.abs.html

openalex publication_date 2004/04/16 · arxiv created 2004/05/20 · arxiv updated 2014/09/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We generalize the notion of parallel transport along paths for abelian bundles to parallel transport along surfaces for abelian gerbes using an embedded Topological Quantum Field Theory (TQFT) approach. We show both for bundles and gerbes with connection that there is a one-to-one correspondence between their local description in terms of locally-defined functions and forms and their non-local description in terms of a suitable class of embedded TQFT's.

Citations

• Cohomologie non abélienne
• Lectures on Special Lagrangian Submanifolds
• Higher Yang-Mills Theory
• Topological structures in string theory
• Topological quantum field theory
• Spin foam models of matter coupled to gravity
• Higher-dimensional algebra and topological quantum field theory
• A functorial approach to differential characters
• Topological quantum field theory
• Differential Geometry of Gerbes