Journal of the European Mathematical Society


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Volume 18, Issue 2, 2016, pp. 281–325
DOI: 10.4171/JEMS/590

Published online: 2016-02-08

Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers

Robert Lipshitz[1] and David Treumann[2]

(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