JournalsjemsVol. 18, No. 2pp. 281–325

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

  • Robert Lipshitz

    Columbia University, New York, USA
  • David Treumann

    Boston College, Chestnut Hill, USA
Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers cover
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Abstract

Let AA be a dg algebra over F2\mathbb F_2 and let MM be a dg AA-bimodule. We show that under certain technical hypotheses on AA, a noncommutative analog of the Hodge-to-de Rham spectral sequence starts at the Hochschild homology of the derived tensor product MALMM \otimes_A^L M and converges to the Hochschild homology of MM. 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