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

Lipshitz, 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 -