Sutured Floer homology, sutured TQFT and noncommutative QFT

Mathews, Daniel V

doi:10.2140/agt.2011.11.2681

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Sutured Floer homology, sutured TQFT and noncommutative QFT

Daniel V Mathews

Algebraic & Geometric Topology 11 (2011) 2681–2739

DOI: 10.2140/agt.2011.11.2681

Abstract

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 $ℤ$ of sutured manifolds $(D^{2} \times S^{1}, F \times S^{1})$ where $F$ is finite. This generalises previous results of the author over $ℤ_{2}$ 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.

Keywords

TQFT, sutured Floer homology

Mathematical Subject Classification 2010

Primary: 57M50

Secondary: 57R58, 57M27, 57R56

References

Publication

Received: 16 February 2011

Revised: 19 June 2011

Accepted: 23 June 2011

Published: 24 September 2011

Authors

Daniel V Mathews
Department of Mathematics Boston College Carney Hall, Room 301 Chestnut Hill MA 02467-3806 USA
http://www.danielmathews.info

Volume 11, issue 5 (2011)