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

Robert Lipshitz; David Treumann

Journal of the European Mathematical Society (2016)

- Volume: 018, Issue: 2, page 281-325
- ISSN: 1435-9855

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topLipshitz, Robert, and Treumann, David. "Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers." Journal of the European Mathematical Society 018.2 (2016): 281-325. <http://eudml.org/doc/277529>.

@article{Lipshitz2016,

abstract = {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 $M\otimes ^L_A M$ 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.},

author = {Lipshitz, Robert, Treumann, David},

journal = {Journal of the European Mathematical Society},

keywords = {Hochschild homology; localization; Smith theory; Heegaard Floer homology; Hochschild homology; localization; Smith theory; Heegaard Floer homology},

language = {eng},

number = {2},

pages = {281-325},

publisher = {European Mathematical Society Publishing House},

title = {Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers},

url = {http://eudml.org/doc/277529},

volume = {018},

year = {2016},

}

TY - JOUR

AU - Lipshitz, Robert

AU - Treumann, David

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

JO - Journal of the European Mathematical Society

PY - 2016

PB - European Mathematical Society Publishing House

VL - 018

IS - 2

SP - 281

EP - 325

AB - 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 $M\otimes ^L_A M$ 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.

LA - eng

KW - Hochschild homology; localization; Smith theory; Heegaard Floer homology; Hochschild homology; localization; Smith theory; Heegaard Floer homology

UR - http://eudml.org/doc/277529

ER -

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