Volume 11, issue 5 (2011)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21, 1 issue

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
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