Explicit Koszul-dualizing bimodules in bordered Heegaard Floer homology

Abstract

We give a combinatorial proof of the quasi-invertibility of $\widehat{CFDD}({\mathbb{I}}_{\mathcal{Z}})$ in bordered Heegaard Floer homology, which implies a Koszul self-duality on the dg-algebra $\mathcal{A}(\mathcal{Z})$, for each pointed matched circle $\mathcal{Z}$. This is done by giving an explicit description of a rank 1 model for $\widehat{CFAA}({\mathbb{I}}_{\mathcal{Z}})$, the quasi-inverse of $\widehat{CFDD}({\mathbb{I}}_{\mathcal{Z}})$. This description is obtained by applying homological perturbation theory to a larger, previously known model of $\widehat{CFAA}({\mathbb{I}}_{\mathcal{Z}})$.

50 pages

References in corpus (4)

• Bimodules in bordered Heegaard Floer homology
• Computing HF^ by factoring mapping classes
• Heegaard Floer homology as morphism spaces
• Explicit Koszul-dualizing bimodules in bordered Heegaard Floer homology

Cited by in corpus (2)

• Explicit Koszul-dualizing bimodules in bordered Heegaard Floer homology
• Combinatorial Proofs in Bordered Heegaard Floer homology