Explicit Koszul-dualizing bimodules in bordered Heegaard Floer homology

Zhan, Bohua

doi:10.2140/agt.2016.16.231

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Explicit Koszul-dualizing bimodules in bordered Heegaard Floer homology

Bohua Zhan

Algebraic & Geometric Topology 16 (2016) 231–266

DOI: 10.2140/agt.2016.16.231

Abstract

We give a combinatorial proof of the quasi-invertibility of $\hat{CFDD} (I_{Z})$ 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 $\hat{CFAA} (I_{Z})$ , the quasi-inverse of $\hat{CFDD} (I_{Z})$ . To obtain this description we apply homological perturbation theory to a larger, previously known model of $\hat{CFAA} (I_{Z})$ .

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

Volume 16, issue 1 (2016)