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

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

2012-03-13

arxiv.org/abs/1203.2963v1

Mathematics

Symplectic Geometry

31 pages, 2 figures

Scientific paper

Let A be a dg algebra over 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 of M with itself 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.

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