Hochschild cohomology of Sullivan algebras and mapping spaces between manifolds

Abstract

Let $e:N^n\to M^m$ be an embedding into a compact manifold $M$. We study the relationship between the homology of the free loop space $LM$ on $M$ and of the space $L_{N}M$ of loops of $M$ based in $N$ and define a shriek map $e_{!}:H_{\ast }(LM,\mathbb{Q})\to H_{\ast }(L_{N}M,\mathbb{Q})$ using Hochschild cohomology and study its properties. We also extend a result of Félix on the injectivity of the induced map ${\mathrm{aut}}_{1}M\to \mathrm{map}(N,M;f)$ on rational homotopy groups when $M$ and $N$ have the same dimension and $f:N\to M$ is a map of non zero degree.

10 pages

References in corpus (1)

• André-Quillen cohomology and rational homotopy of function spaces