Volume 16, issue 1 (2016)

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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 $\stackrel{̂}{\mathit{CFDD}}\left({\mathbb{I}}_{\mathsc{Z}}\right)$ in bordered Heegaard Floer homology, which implies a Koszul self-duality on the dg-algebra $\mathsc{A}\left(\mathsc{Z}\right)$, for each pointed matched circle $\mathsc{Z}$. We do this by giving an explicit description of a rank 1 model for $\stackrel{̂}{\mathit{CFAA}}\left({\mathbb{I}}_{\mathsc{Z}}\right)$, the quasi-inverse of $\stackrel{̂}{\mathit{CFDD}}\left({\mathbb{I}}_{\mathsc{Z}}\right)$. To obtain this description we apply homological perturbation theory to a larger, previously known model of $\stackrel{̂}{\mathit{CFAA}}\left({\mathbb{I}}_{\mathsc{Z}}\right)$.

Keywords
bordered Heegaard Floer homology
Primary: 57R58
Secondary: 57R56
Supplementary material

Cancellation diagrams