The cohomology algebra of certain free loop spaces

Toshihiro Yamaguchi; Katsuhiko Kuribayashi

Fundamenta Mathematicae (1997)

  • Volume: 154, Issue: 1, page 57-73
  • ISSN: 0016-2736

Abstract

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Let X be a simply connected space and LX the space of free loops on X. We determine the mod p cohomology algebra of LX when the mod p cohomology of X is generated by one element or is an exterior algebra on two generators. We also provide lower bounds on the dimensions of the Hodge decomposition factors of the rational cohomology of LX when the rational cohomology of X is a graded complete intersection algebra. The key to both of these results is the identification of an important subalgebra of the Hochschild homology of a graded complete intersection algebra over a field.

How to cite

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Yamaguchi, Toshihiro, and Kuribayashi, Katsuhiko. "The cohomology algebra of certain free loop spaces." Fundamenta Mathematicae 154.1 (1997): 57-73. <http://eudml.org/doc/212227>.

@article{Yamaguchi1997,
abstract = {Let X be a simply connected space and LX the space of free loops on X. We determine the mod p cohomology algebra of LX when the mod p cohomology of X is generated by one element or is an exterior algebra on two generators. We also provide lower bounds on the dimensions of the Hodge decomposition factors of the rational cohomology of LX when the rational cohomology of X is a graded complete intersection algebra. The key to both of these results is the identification of an important subalgebra of the Hochschild homology of a graded complete intersection algebra over a field.},
author = {Yamaguchi, Toshihiro, Kuribayashi, Katsuhiko},
journal = {Fundamenta Mathematicae},
keywords = {Hodge decomposition factors},
language = {eng},
number = {1},
pages = {57-73},
title = {The cohomology algebra of certain free loop spaces},
url = {http://eudml.org/doc/212227},
volume = {154},
year = {1997},
}

TY - JOUR
AU - Yamaguchi, Toshihiro
AU - Kuribayashi, Katsuhiko
TI - The cohomology algebra of certain free loop spaces
JO - Fundamenta Mathematicae
PY - 1997
VL - 154
IS - 1
SP - 57
EP - 73
AB - Let X be a simply connected space and LX the space of free loops on X. We determine the mod p cohomology algebra of LX when the mod p cohomology of X is generated by one element or is an exterior algebra on two generators. We also provide lower bounds on the dimensions of the Hodge decomposition factors of the rational cohomology of LX when the rational cohomology of X is a graded complete intersection algebra. The key to both of these results is the identification of an important subalgebra of the Hochschild homology of a graded complete intersection algebra over a field.
LA - eng
KW - Hodge decomposition factors
UR - http://eudml.org/doc/212227
ER -

References

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