The Hochschild cohomology ring of the singular cochain algebra of a space

Katsuhiko Kuribayashi[1]

  • [1] Shinshu University, Faculty of Science, Department of Mathematical Sciences, Matsumoto, Nagano 390-8621, Japan

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 5, page 1779-1805
  • ISSN: 0373-0956

Abstract

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We determine the algebra structure of the Hochschild cohomology of the singular cochain algebra with coefficients in a field on a space whose cohomology is a polynomial algebra. A spectral sequence calculation of the Hochschild cohomology is also described. In particular, when the underlying field is of characteristic two, we determine the associated bigraded Batalin-Vilkovisky algebra structure on the Hochschild cohomology of the singular cochain on a space whose cohomology is an exterior algebra.

How to cite

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Kuribayashi, Katsuhiko. "The Hochschild cohomology ring of the singular cochain algebra of a space." Annales de l’institut Fourier 61.5 (2011): 1779-1805. <http://eudml.org/doc/219770>.

@article{Kuribayashi2011,
abstract = {We determine the algebra structure of the Hochschild cohomology of the singular cochain algebra with coefficients in a field on a space whose cohomology is a polynomial algebra. A spectral sequence calculation of the Hochschild cohomology is also described. In particular, when the underlying field is of characteristic two, we determine the associated bigraded Batalin-Vilkovisky algebra structure on the Hochschild cohomology of the singular cochain on a space whose cohomology is an exterior algebra.},
affiliation = {Shinshu University, Faculty of Science, Department of Mathematical Sciences, Matsumoto, Nagano 390-8621, Japan},
author = {Kuribayashi, Katsuhiko},
journal = {Annales de l’institut Fourier},
keywords = {Hochschild cohomology; singular cochain algebra; Batalin-Vilkovisky algebra; Koszul-Tate resolution; Hochschild cohomology rings; singular cochain algebras; Batalin-Vilkovisky algebras; Koszul-Tate resolutions; spectral sequences},
language = {eng},
number = {5},
pages = {1779-1805},
publisher = {Association des Annales de l’institut Fourier},
title = {The Hochschild cohomology ring of the singular cochain algebra of a space},
url = {http://eudml.org/doc/219770},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Kuribayashi, Katsuhiko
TI - The Hochschild cohomology ring of the singular cochain algebra of a space
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 5
SP - 1779
EP - 1805
AB - We determine the algebra structure of the Hochschild cohomology of the singular cochain algebra with coefficients in a field on a space whose cohomology is a polynomial algebra. A spectral sequence calculation of the Hochschild cohomology is also described. In particular, when the underlying field is of characteristic two, we determine the associated bigraded Batalin-Vilkovisky algebra structure on the Hochschild cohomology of the singular cochain on a space whose cohomology is an exterior algebra.
LA - eng
KW - Hochschild cohomology; singular cochain algebra; Batalin-Vilkovisky algebra; Koszul-Tate resolution; Hochschild cohomology rings; singular cochain algebras; Batalin-Vilkovisky algebras; Koszul-Tate resolutions; spectral sequences
UR - http://eudml.org/doc/219770
ER -

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