AGT 4 (2004) Paper 14 (Abstract)

Algebraic and Geometric Topology 4 (2004), paper no. 14, pages 243-272.

TQFT's and gerbes

Roger Picken

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

AMS subject classification. Primary: 55R65. Secondary: 53C29.

DOI: 10.2140/agt.2004.4.243

E-print: arXiv:math.DG/0302065

Submitted: 2 March 2004. Accepted: 15 April 2004. Published: 16 April 2004.

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Roger Picken
Departamento de Matematica and CEMAT - Centro de Matematica e Aplicacoes
Instituto Superior Tecnico, Av Rovisco Pais
1049-001 Lisboa, Portugal
Email: rpicken@math.ist.utl.pt

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