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2011 Sutured Floer homology, sutured TQFT and noncommutative QFT
Daniel V Mathews
Algebr. Geom. Topol. 11(5): 2681-2739 (2011). DOI: 10.2140/agt.2011.11.2681


We define a “sutured topological quantum field theory”, motivated by the study of sutured Floer homology of product 3–manifolds, and contact elements. We study a rich algebraic structure of suture elements in sutured TQFT, showing that it corresponds to contact elements in sutured Floer homology. We use this approach to make computations of contact elements in sutured Floer homology over of sutured manifolds (D2×S1,F×S1) where F is finite. This generalises previous results of the author over 2 coefficients. Our approach elaborates upon the quantum field theoretic aspects of sutured Floer homology, building a noncommutative Fock space, together with a bilinear form deriving from a certain combinatorial partial order; we show that the sutured TQFT of discs is isomorphic to this Fock space.


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Daniel V Mathews. "Sutured Floer homology, sutured TQFT and noncommutative QFT." Algebr. Geom. Topol. 11 (5) 2681 - 2739, 2011.


Received: 16 February 2011; Revised: 19 June 2011; Accepted: 23 June 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1271.57048
MathSciNet: MR2846909
Digital Object Identifier: 10.2140/agt.2011.11.2681

Primary: 57M50
Secondary: 57M27 , 57R56 , 57R58

Keywords: sutured Floer homology , TQFT

Rights: Copyright © 2011 Mathematical Sciences Publishers


Vol.11 • No. 5 • 2011
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