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Refined invariants and TQFTs from Homfly skein theory


Beliakova, A (1999). Refined invariants and TQFTs from Homfly skein theory. Journal of Knot Theory and Its Ramifications, 8(5):569-587.

Abstract

We work in the reduced SU(N, K) modular category as constructed recently by Blanchet. We define spin type and cohomological refinements of the Turaev-Viro invariants of closed oriented 3-manifolds and give a formula relating them to Blanchet's invariants. Roberts' definition of the Turaev-Viro state sum is exploited. Furthermore, we construct refined Turaev-Viro and Reshetikhin-Turaev TQFTs and study the relationship between them.

Abstract

We work in the reduced SU(N, K) modular category as constructed recently by Blanchet. We define spin type and cohomological refinements of the Turaev-Viro invariants of closed oriented 3-manifolds and give a formula relating them to Blanchet's invariants. Roberts' definition of the Turaev-Viro state sum is exploited. Furthermore, we construct refined Turaev-Viro and Reshetikhin-Turaev TQFTs and study the relationship between them.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Modular categories; Turaev-Viro invariants; spin structures; Heegaard splitting
Language:English
Date:1999
Deposited On:19 Apr 2010 10:34
Last Modified:05 Apr 2016 13:26
Publisher:World Scientific Publishing
ISSN:0218-2165
Additional Information:Electronic version of an article published as [ J. Knot Theory Ramifications 8 (1999), no. 5, 569--587] © 1999 copyright World Scientific Publishing Company [http://www.worldscinet.com/jktr/jktr.shtml]
Publisher DOI:https://doi.org/10.1142/S0218216599000390

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