Homology, Homotopy and Applications
Volume 15 (2013)
Localisations of cobordism categories and invertible TFTs in dimension two
Pages: 195 – 225
Cobordism categories have played an important role in classical geometry and more recently in mathematical treatments of quantum field theory. Here we will compute localisations of two-dimensional discrete cobordism categories. This allows us, up to equivalence, to determine the category of invertible two-dimensional topological field theories in the sense of Atiyah. We are able to treat the orientable, non-orientable, closed, and open cases.
topological quantum field theory, non-orientable surface, pointed monoidal category
2010 Mathematics Subject Classification
18D10, 57R56, 81T45