Gerbes and homotopy quantum field theories
Preprint
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
All Related Versions
This publication has 9 references indexed in Scilit:
- HOMOTOPY QUANTUM FIELD THEORIES AND THE HOMOTOPY COBORDISM CATEGORY IN DIMENSION 1 + 1Journal of Knot Theory and Its Ramifications, 2003
- REPRESENTATIONS OF THE HOMOTOPY SURFACE CATEGORY OF A SIMPLY CONNECTED SPACEJournal of Knot Theory and Its Ramifications, 2000
- Geometry of Deligne cohomologyInventiones Mathematicae, 1997
- Bundle GerbesJournal of the London Mathematical Society, 1996
- AN AXIOMATIC DEFINITION OF HOLONOMYInternational Journal of Mathematics, 1994
- Higher algebraic structures and quantizationCommunications in Mathematical Physics, 1994
- Loop Spaces, Characteristic Classes and Geometric Quantization1993
- Holonomy and path structures in general relativity and Yang-Mills theoryInternational Journal of Theoretical Physics, 1991
- Differential characters and geometric invariants1985