TQFT’s and gerbes

Picken, Roger

doi:10.2140/agt.2004.4.243

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TQFT's and gerbes

Roger Picken

Algebraic & Geometric Topology 4 (2004) 243–272

DOI: 10.2140/agt.2004.4.243

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

References

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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

Volume 4, issue 1 (2004)