Hochschild cohomology of Sullivan algebras and mapping spaces between manifolds

2020/08/25 by J.-B. Gatsinzi, Gatsinzi, J. -B.
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2008.10878

Abstract

Let e: Nⁿ → 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, ℚ) → H_*( L_NM, ℚ) using Hochschild cohomology and study its properties. We also extend a result of Félix on the injectivity of the induced map aut₁M → map(N, M; f ) on rational homotopy groups when M and N have the same dimension and f: N→ M is a map of non zero degree.

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