On the real cohomology of spaces of free loops on manifolds

Katsuhiko Kuribayashi

Fundamenta Mathematicae (1996)

  • Volume: 150, Issue: 2, page 173-188
  • ISSN: 0016-2736

Abstract

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Let LX be the space of free loops on a simply connected manifold X. When the real cohomology of X is a tensor product of algebras generated by a single element, we determine the algebra structure of the real cohomology of LX by using the cyclic bar complex of the de Rham complex Ω(X) of X. In consequence, the algebra generators of the real cohomology of LX can be represented by differential forms on LX through Chen’s iterated integral map. Let 𝕋 be the circle group. The 𝕋 -equivariant cohomology of LX is also studied in terms of the cyclic homology of Ω(X).

How to cite

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Kuribayashi, Katsuhiko. "On the real cohomology of spaces of free loops on manifolds." Fundamenta Mathematicae 150.2 (1996): 173-188. <http://eudml.org/doc/212168>.

@article{Kuribayashi1996,
abstract = {Let LX be the space of free loops on a simply connected manifold X. When the real cohomology of X is a tensor product of algebras generated by a single element, we determine the algebra structure of the real cohomology of LX by using the cyclic bar complex of the de Rham complex Ω(X) of X. In consequence, the algebra generators of the real cohomology of LX can be represented by differential forms on LX through Chen’s iterated integral map. Let $\mathbb \{T\}$ be the circle group. The $\mathbb \{T\}$-equivariant cohomology of LX is also studied in terms of the cyclic homology of Ω(X).},
author = {Kuribayashi, Katsuhiko},
journal = {Fundamenta Mathematicae},
keywords = {space of free loops; simply connected manifold; real cohomology; cyclic bar complex; de Rham complex; iterated integral map},
language = {eng},
number = {2},
pages = {173-188},
title = {On the real cohomology of spaces of free loops on manifolds},
url = {http://eudml.org/doc/212168},
volume = {150},
year = {1996},
}

TY - JOUR
AU - Kuribayashi, Katsuhiko
TI - On the real cohomology of spaces of free loops on manifolds
JO - Fundamenta Mathematicae
PY - 1996
VL - 150
IS - 2
SP - 173
EP - 188
AB - Let LX be the space of free loops on a simply connected manifold X. When the real cohomology of X is a tensor product of algebras generated by a single element, we determine the algebra structure of the real cohomology of LX by using the cyclic bar complex of the de Rham complex Ω(X) of X. In consequence, the algebra generators of the real cohomology of LX can be represented by differential forms on LX through Chen’s iterated integral map. Let $\mathbb {T}$ be the circle group. The $\mathbb {T}$-equivariant cohomology of LX is also studied in terms of the cyclic homology of Ω(X).
LA - eng
KW - space of free loops; simply connected manifold; real cohomology; cyclic bar complex; de Rham complex; iterated integral map
UR - http://eudml.org/doc/212168
ER -

References

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