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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Sutured Floer homology, sutured TQFT and noncommutative QFT

Daniel V Mathews

Algebraic & Geometric Topology 11 (2011) 2681–2739

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.

TQFT, sutured Floer homology
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 57R58, 57M27, 57R56
Received: 16 February 2011
Revised: 19 June 2011
Accepted: 23 June 2011
Published: 24 September 2011
Daniel V Mathews
Department of Mathematics
Boston College
Carney Hall, Room 301
Chestnut Hill MA 02467-3806