Algebraic and Geometric Topology 4 (2004), paper no. 21, pages 407-437.

Gerbes and homotopy quantum field theories

Ulrich Bunke, Paul Turner, Simon Willerton

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

AMS subject classification. Primary: 55P48. Secondary: 57R56, 81T70.

DOI: 10.2140/agt.2004.4.407

E-print: arXiv:math.AT/0201116

Submitted: 8 June 2004. Accepted: 10 June 2004. Published: 24 June 2004.

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Ulrich Bunke, Paul Turner, Simon Willerton
Mathematisches Institut, Universitaet Goettingen, 37073 Goettingen, Germany

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

Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH, England

Email: bunke@uni-math.gwdg.de, paul@ma.hw.ac.uk, s.willerton@shef.ac.uk

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