Work

Geodesic Models for Loop Spaces on Riemannian Manifolds

Year: 2026

Type: preprint

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 $M$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.15668

Authors: Bahri, Abbas, Cohen, Fred, Ghazel, Moncef, Kallel, Sadok

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, American University of Sharjah

Award: G8677745766

OpenAlex ID: W7221811704

Cites: 1

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Related to: 10