Gerbes and homotopy quantum field theories

Bunke, Ulrich; Turner, Paul; Willerton, Simon

doi:10.2140/agt.2004.4.407

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Gerbes and homotopy quantum field theories

Ulrich Bunke, Paul Turner and Simon Willerton

Algebraic & Geometric Topology 4 (2004) 407–437

DOI: 10.2140/agt.2004.4.407

arXiv: math.AT/0201116

Abstract

For smooth finite dimensional manifolds, we characterise gerbes with connection as functors on a certain surface cobordism category. This allows us to relate gerbes with connection to Turaev’s $(1 + 1)$ –dimensional homotopy quantum field theories, and we show that flat gerbes are related to a specific class of rank one homotopy quantum field theories.

Keywords

gerbe, differential character, homotopy quantum field theory

Mathematical Subject Classification 2000

Primary: 55P48

Secondary: 57R56, 81T70

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Publication

Received: 8 June 2004

Accepted: 10 June 2004

Published: 24 June 2004

Authors

Ulrich Bunke
Mathematisches Institut Universität Göttingen 37073 Göttingen Germany

Paul Turner
Department of Mathematics Heriot-Watt University Edinburgh EH14 4AS Scotland

Simon Willerton
Department of Pure Mathematics University of Sheffield Sheffield S3 7RH England

Volume 4, issue 1 (2004)