2002/04/11 by Yves Félix, Yves Felix, Felix, Yves +3
Mathematics · #55P10 #55P35 #55P62 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:55P10 #msc:55P35 #msc:55P62
paper · pdf · doi:10.48550/arxiv.math/0204152
arxiv created 2002/04/11 · openalex publication_date 2002/04/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a simply-connected closed oriented N-dimensional manifold. We prove that for any field of coefficients there exists a natural homomorphism of commutative graded algebras Ψ: H_∗ (Ωaut1 M) → H∗ +N(MS1) where H_∗ (MS1) is the loop algebra defined by Chas-Sullivan. As usual aut1 X (resp. ΩX) denotes the monoid of the self-equivalences homotopic to the identity map (resp. the space of based loops) of the space X. Moreover, if \bk is of characteristic zero, Ψ yields isomorphisms πn(Ωaut1 M) ⊗ \bk ≅ \hHn+N(1) where ⊕l=1^∞ \hHn(l) denotes the Hodge decomposition on H^∗ (M S1).