Localisations of cobordism categories and invertible TFTs in dimension two
arXiv:1307.6886
Abstract
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.
30 pages, accepted for publication by Homology, Homotopy and Applications