On the cohomology algebra of free loop spaces

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dc.creatorNdombol, Bitjong
dc.creatorThomas, Jean-Claude
dc.date2001-09-20
dc.date.accessioned2026-07-07T04:43:28Z
dc.date.available2026-07-07T04:43:28Z
dc.descriptionLet $X$ be a simply connected space and $\Bbb K$ be any field. The normalized singular cochains $N^*(X; {\Bbb K})$ admit a natural strongly homotopy commutative algebra structure, which induces a natural product on the Hochschild homology $HH_* N^*X$ of the space $X$. We prove that, endowed with this product, $HH_*N^*X$ is isomorphic to the cohomology algebra of the free loop space of $X$ with coefficients in $\Bbb K$. We also show how to construct a simpler Hochschild complex which allows direct computation.
dc.description21 pages, to appear in Topology
dc.identifierhttps://arxiv.org/abs/math/0109145
dc.identifierhttp://arxiv.org/abs/math/0109145
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62235
dc.subjectAlgebraic Topology
dc.subjectAlgebraic Geometry
dc.subjectK-Theory and Homology
dc.subject57T30, 54C35, 55S20
dc.titleOn the cohomology algebra of free loop spaces
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