Remarks on the geometry and the topology of the loop spaces $H^{s}(S^1, N),$ for $s\leq 1/2.$

International Journal of Maps in Mathematics - IJMM

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Title Remarks on the geometry and the topology of the loop spaces $H^{s}(S^1, N),$ for $s\leq 1/2.$
 
Creator Magnot, Jean-Pierre
 
Description We first show that, for a fixed locally compact manifold $N,$ the space $L^2(S^1,N)$ has not the homotopy type of 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. Then, we show that the spaces $H^s(S^1,N)$ carry a natural structure of Fr\"olicher space, equipped with a Riemannian metric, which motivates the definition of Riemannian diffeological space.
 
Publisher Bayram Şahin
 
Date 2019-03-22
 
Type info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
 
Format application/pdf
 
Identifier http://www.journalmim.com/index.php/ijmm/article/view/29
 
Source International Journal of Maps in Mathematics - IJMM; Vol 2 No 1 (2019): International Journal of Maps in Mathematics; 14-37
2636-7467
 
Language eng
 
Relation http://www.journalmim.com/index.php/ijmm/article/view/29/24
 
Rights Copyright (c) 2019 International Journal of Maps in Mathematics - IJMM
 

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