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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Patrick M. Gilmer and Xuanye Wang
Journal: Proc. Amer. Math. Soc. 142 (2014), 2915-2920
MSC (2010): Primary 57R56; Secondary 57M99
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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Additional Information

Patrick M. Gilmer
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: gilmer@math.lsu.edu

Xuanye Wang
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: xuanye.wang@utexas.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-12022-3
PII: S 0002-9939(2014)12022-3
Keywords: Quantization functor, universal construction, $p_1$-structure, topological quantum field theory
Received by editor(s): January 19, 2012
Received by editor(s) in revised form: August 27, 2012
Published electronically: April 15, 2014
Additional Notes: The first author was partially supported by NSF-DMS-0905736
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.