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Geodesic Models for Loop Spaces on Riemannian Manifolds

  • Abbas Bahri
  • Fred Cohen
  • Moncef Ghazel
  • Sadok Kallel
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Abstract

A topological group, defined in terms of ``composable minimal geodesics'' is constructed and shown to be homotopy equivalent to the pointed loop space of a path-connected, simply connected Riemannian manifold M of positive convexity radius. This construction is analogous to John Milnor's free group model for the pointed loop space of a connected simplicial complex. Related models built from composable minimal geodesics are also obtained for the free loop space of M and for the space of maps from any finite two-dimensional CW-complex into M.

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Cite

BibTeXRIS
BibTeX
@misc{bahri2026geodesic,
  title = {{Geodesic Models for Loop Spaces on Riemannian Manifolds}},
  author = {Abbas Bahri and Fred Cohen and Moncef Ghazel and Sadok Kallel},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15668},
  eprint = {2610.15668},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15668},
}
RIS
TY  - UNPB
TI  - Geodesic Models for Loop Spaces on Riemannian Manifolds
AU  - Abbas Bahri
AU  - Fred Cohen
AU  - Moncef Ghazel
AU  - Sadok Kallel
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15668
UR  - https://arxiv.org/abs/2610.15668
AB  - A topological group, defined in terms of ``composable minimal geodesics'' is constructed and shown to be homotopy equivalent to the pointed loop space of a path-connected, simply connected Riemannian manifold M of positive convexity radius. This construction is analogous to John Milnor's free group model for the pointed loop space of a connected simplicial complex. Related models built from composable minimal geodesics are also obtained for the free loop space of M and for the space of maps from any finite two-dimensional CW-complex into M.
ER  -