Homology, Homotopy and Applications

Volume 15 (2013)

Number 2

Localisations of cobordism categories and invertible TFTs in dimension two

Pages: 195 – 225

DOI: http://dx.doi.org/10.4310/HHA.2013.v15.n2.a13

Authors

R. Juer (Mathematical Institute, University of Oxford, United Kingdom)

U. Tillmann (Mathematical Institute, University of Oxford, United Kingdom)

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.

Keywords

topological quantum field theory, non-orientable surface, pointed monoidal category

2010 Mathematics Subject Classification

18D10, 57R56, 81T45

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