Volume 4, issue 1 (2004)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
TQFT's and gerbes

Roger Picken

Algebraic & Geometric Topology 4 (2004) 243–272

arXiv: math.DG/0302065

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.

Keywords
Topological Quantum Field Theory, TQFT, gerbes, parallel transport
Mathematical Subject Classification 2000
Primary: 55R65
Secondary: 53C29
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Publication
Received: 2 March 2004
Accepted: 15 April 2004
Published: 16 April 2004
Authors
Roger Picken
Departamento de Matemática and CEMAT - Centro de Matemática e Aplicações
Instituto Superior Técnico
Av Rovisco Pais
1049-001 Lisboa, Portugal