The space of non-degenerate closed curves in a Riemannian manifold

2012/09/18 by Jacob Mostovoy, Mostovoy, Jacob, Rustam Sadykov +1
Mathematics · Physics and Astronomy · #53A04 #Advanced Differential Geometry Research #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Waves and Solitons #math.AT #math.DG #msc:53A04

paper · pdf · doi:10.48550/arxiv.1209.4109

9 pages 1 figure

arxiv created 2012/09/18 · openalex publication_date 2012/09/18 · arxiv updated 2012/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let LM be the semigroup of non-degenerate based loops with a fixed initial/final frame in a Riemannian manifold M of dimension at least three. We compare the topology of LM to that of the loop space Omega FTM on the bundle of frames in the tangent bundle of M. We show that Omega FTM is the group completion of LM, and prove that it is obtained by localizing LM with respect to adding a "small twist".

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