Volume 4, issue 1 (2004)

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Gerbes and homotopy quantum field theories

Ulrich Bunke, Paul Turner and Simon Willerton

Algebraic & Geometric Topology 4 (2004) 407–437

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