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- W2230797735 abstract "We first show that, for a fixed locally compact manifold $N,$ the space $L^2(S^1,N)$ has not the homotopy type odf the classical loop space $C^infty(S^1,N),$ by two theorems: - the inclusion $C^infty(S^1,N) subset L^2(S^1,N)$ is null homotopic if $N $ is connected, - the space $L^2(S^1,N)$ is contractible if $N$ is compact and connected. After this first remark, we show that the spaces $H^s(S^1,N)$ carry a natural structure of Frolicher space, equipped with a Riemannian metric, which motivates the definition of Riemannian Frolicher space." @default.
- W2230797735 created "2016-06-24" @default.
- W2230797735 creator A5034803508 @default.
- W2230797735 date "2015-07-21" @default.
- W2230797735 modified "2023-09-27" @default.
- W2230797735 title "Remarks on the geometry and the topology of the loop spaces $H^{s}(S^1, N),$ for $sleq 1/2.$" @default.
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