Remarks on the geometry and the topology of the loop spaces $H^{s}(S^1, N),$ for $s\leq 1/2.$ - Archive ouverte HAL Access content directly
Journal Articles International Journal of Maps in Mathematics Year : 2019

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

Abstract

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 ∞ (S 1 , N), by two theorems:-the inclusion C ∞ (S 1 , N) ⊂ 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 Frölicher space, equipped with a Riemannian metric, which motivates the definition of Riemannian diffeo-logical space.
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Dates and versions

hal-02285964 , version 1 (13-09-2019)

Identifiers

  • HAL Id : hal-02285964 , version 1

Cite

Jean-Pierre Magnot. 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, 2019, pp.14 - 37. ⟨hal-02285964⟩
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