Explicit Koszul-dualizing bimodules in bordered Heegaard Floer homology

@article{Zhan2016ExplicitKB,
  title={Explicit Koszul-dualizing bimodules in bordered Heegaard Floer homology},
  author={Bohua Zhan},
  journal={Algebraic \& Geometric Topology},
  year={2016},
  volume={16},
  pages={231-266}
}
  • Bohua Zhan
  • Published 25 March 2014
  • Mathematics
  • Algebraic & Geometric Topology
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… 
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We compare two different types of mapping class invariants: Hochschild homology of $A_\infty$ bimodule coming from bordered Heegaard Floer homology, and fixed point Floer cohomology. Having done

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