Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers
Robert Lipshitz
Columbia University, New York, USADavid Treumann
Boston College, Chestnut Hill, USA
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Abstract
Let be a dg algebra over and let be a dg -bimodule. We show that under certain technical hypotheses on , a noncommutative analog of the Hodge-to-de Rham spectral sequence starts at the Hochschild homology of the derived tensor product and converges to the Hochschild homology of . 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.
Cite this article
Robert Lipshitz, David Treumann, Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers. J. Eur. Math. Soc. 18 (2016), no. 2, pp. 281–325
DOI 10.4171/JEMS/590