Gerbes and homotopy quantum field theories

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.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-21.abs.html

References in corpus (1)

• A functorial approach to differential characters

Cited by in corpus (6)

• TQFT's and gerbes
• Smooth one-dimensional topological field theories are vector bundles with connection
• Smooth Functorial Field Theories from B-Fields and D-Branes
• A functorial approach to differential characters
• Gerbes in Geometry, Field Theory, and Quantisation
• Two-Dimensional Extended Homotopy Field Theories