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- W1693951984 abstract "Let $M$ be a simply-connected closed oriented $N$-dimensional manifold. We prove that for any field of coefficients $l!k$ there exists a natural homomorphism of commutative graded algebras $Gamma : H_* (Omega mbox {aut}_1 M) to mathbb H_{*}(M^{S^1})$ where $mathbb H_*(M^{S^1})= H_{* +N}(M^{S^1})$ is the loop algebra defined by Chas and Sullivan. As usual $mbox {aut}_1 X$ denotes the monoid of self-equivalences homotopic to the identity, and $Omega X$ the space of based loops. When $l!k$ is of characteristic zero, $Gamma$ yields isomorphisms $H^{n+N}_{(1)}(M^{S^1}) stackrel {cong }{to } (pi _n(Omega mbox {aut}_1 M) otimes l!k)^vee$ where $bigoplus _{l=1}^infty H^n_{(l)}(M^{S^1})$ denotes the Hodge decomposition on $H^* (M ^{S^1})$." @default.
- W1693951984 created "2016-06-24" @default.
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- W1693951984 date "2003-05-28" @default.
- W1693951984 modified "2023-09-25" @default.
- W1693951984 title "Monoid of self-equivalences and free loop spaces" @default.
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- W1693951984 doi "https://doi.org/10.1090/s0002-9939-03-07018-7" @default.
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