Journal of the European Mathematical Society
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Published online: 2016-02-08
Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double coversRobert Lipshitz and David Treumann (1) Columbia University, New York, USA
(2) Boston College, Chestnut Hill, USA
Let $A$ be a dg algebra over $\mathbb F_2$ and let $M$ be a dg $A$-bimodule. We show that under certain technical hypotheses on $A$, a noncommutative analog of the Hodge-to-de Rham spectral sequence starts at the Hochschild homology of the derived tensor product $M \otimes_A^L M$ and converges to the Hochschild homology of $M$. We apply this result to bordered Heegaard Floer theory, giving spectral sequences associated to Heegaard Floer homology groups of certain branched and unbranched double covers.
Keywords: Hochschild homology, localization, Smith theory, Heegaard Floer homology
Lipshitz Robert, Treumann David: Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers. J. Eur. Math. Soc. 18 (2016), 281-325. doi: 10.4171/JEMS/590