# 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

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topYamaguchi, 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 -

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