@article {
author = {Gatsinzi, J.-B.},
title = {Hochschild cohomology of Sullivan algebras and mapping spaces between manifolds},
journal = {Journal of the Iranian Mathematical Society},
volume = {3},
number = {1},
pages = {23-32},
year = {2022},
publisher = {Iranian Mathematical Society},
issn = {2717-1612},
eissn = {2717-1612},
doi = {10.30504/jims.2023.366483.1078},
abstract = {Let $e: N^n \rightarrow M ^m$ be an embedding of closed, oriented manifolds of dimension $n$ and $m$ respectively. We study the relationship between the homology of the free loop space $LM$ on $M$ and of the space $L_NM$ of loops of $M$ based in $N$ and define a shriek map $ H_*(e)_{!}: H_*( LM, \mathbb{Q}) \rightarrow H_*( L_NM, \mathbb{Q})$ using Hochschild cohomology and study its properties. In particular we extend a result of F\'elix on the injectivity of the map induced by $ \aut_1M \rightarrow \map(N, M; f ) $ on rational homotopy groups when $M$ and $N$ have the same dimension and $ f: N\rightarrow M $ is a map of non zero degree.},
keywords = {Loop space homology,Poincar\' e duality,Hochschild cohomology},
url = {https://jims.ims.ir/article_169711.html},
eprint = {https://jims.ims.ir/article_169711_ce0f801a6ce58f4528b3c6176c04b639.pdf}
}