#### 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 $\left(1+1\right)$–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