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

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

2012-01-09

arxiv.org/abs/1201.1921v1

Mathematics

Geometric Topology

5 pages, 1 figure

Scientific paper

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. The purpose of this paper is to explain that without this extra structure, one would not get finite dimensionality. To this purpose, we perform the universal construction of [BHMV95] without the extra structure and show that the resulting quantization functor assigns an infinite dimensional vector space to the torus.

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