TQFT’s and gerbes

Picken, Roger¹

¹Departamento de Matemática and CEMAT - Centro de Matemática e Aplicações, Instituto Superior Técnico, Av Rovisco Pais, 1049-001 Lisboa, Portugal

Algebraic and Geometric Topology, Tome 4 (2004) no. 1, pp. 243-272

Résumé

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.

Détail

DOI : 10.2140/agt.2004.4.243

Keywords: Topological Quantum Field Theory, TQFT, gerbes, parallel transport

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