On the cohomology algebra of free loop spaces

Details On the cohomology algebra of free loop spaces On the cohomology algebra of free loop spaces

2001-09-20

arxiv.org/abs/math/0109145v1

Mathematics

Algebraic Topology

21 pages, to appear in Topology

Scientific paper

Let $X$ 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.

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