Extra structure and the universal construction for the Witten-Reshetikhin-Turaev TQFT

Gilmer, Patrick; Wang, Xuanye

doi:10.1090/S0002-9939-2014-12022-3

Extra structure and the universal construction for the Witten-Reshetikhin-Turaev TQFT
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by Patrick M. Gilmer and Xuanye Wang

Proc. Amer. Math. Soc. 142 (2014), 2915-2920

DOI: https://doi.org/10.1090/S0002-9939-2014-12022-3

Published electronically: April 15, 2014

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Abstract:

A TQFT is a functor from a cobordism category to the category of vector spaces satisfying certain properties. An important property is that the vector spaces should be finite dimensional. For the WRT TQFT, the relevant $2+1$-cobordism category is built from manifolds which are equipped with an extra structure such as a $p_1$-structure or an extended manifold structure. We perform the universal construction of Blanchet, Habegger, Masbaum, and Vogel (1992) on a cobordism category without this extra structure and show that the resulting quantization functor assigns an infinite dimensional vector space to the torus.

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