Volume 16, issue 1 (2016)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Explicit Koszul-dualizing bimodules in bordered Heegaard Floer homology

Bohua Zhan

Algebraic & Geometric Topology 16 (2016) 231–266
Abstract

We give a combinatorial proof of the quasi-invertibility of CFDD̂(IZ) in bordered Heegaard Floer homology, which implies a Koszul self-duality on the dg-algebra A(Z), for each pointed matched circle Z. We do this by giving an explicit description of a rank 1 model for CFAÂ(IZ), the quasi-inverse of CFDD̂(IZ). To obtain this description we apply homological perturbation theory to a larger, previously known model of CFAÂ(IZ).

Keywords
bordered Heegaard Floer homology
Mathematical Subject Classification 2010
Primary: 57R58
Secondary: 57R56
Supplementary material

Cancellation diagrams

References
Publication
Received: 27 May 2014
Revised: 22 May 2015
Accepted: 5 June 2015
Published: 23 February 2016
Authors
Bohua Zhan
Department of Mathematics
Massachusetts Institute of Technology
Building E18, Room 306
77 Massachusetts Avenue
Cambridge, MA 02139-4307
USA