On "small geodesics" and free loop spaces

2008/06/03 by Abbas Bahri, A. Bahri, Fred Cohen +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary: 55R99 #Secondary: 58D99 #math.AT #msc:55R99 #msc:58D99

paper · pdf · doi:10.48550/arxiv.0806.0637

arxiv created 2008/06/03 · openalex publication_date 2008/06/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A topological group is constructed which is homotopy equivalent to the pointed loop space of a path-connected Riemannian manifold M and which is given in terms of "composable small geodesics" on M. This model is analogous to J. Milnor's free group construction \citeMilnor which provides a model for the pointed loop space of a connected simplicial complex. Related function spaces are constructed from "composable small geodesics" which provide models for the free loop space of M as well as the space of continuous maps from a surface to M.

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