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.
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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. 281–325DOI 10.4171/JEMS/590