论文标题
沙利文代数的Hochschild协同学和歧管之间的映射空间
Hochschild cohomology of Sullivan algebras and mapping spaces between manifolds
论文作者
论文摘要
令$ e：n^n \ rightarrow m $ $是嵌入紧凑的歧管$ m $中的嵌入。 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 $ e_{!}: H_*( LM, \mathbb{Q}) \rightarrow H_*( L_NM, \mathbb{Q})$ using Hochschild cohomology and研究其特性。 We also extend a result of Félix on the injectivity of the induced map $ \mathrm{aut}_1M \rightarrow \mathrm{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.
Let $e: N^n \rightarrow 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 $L_NM$ of loops of $M$ based in $N$ and define a shriek map $ e_{!}: H_*( LM, \mathbb{Q}) \rightarrow H_*( L_NM, \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}_1M \rightarrow \mathrm{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.
