On "small geodesics" and free loop spaces

Details On "small geodesics" and free loop spaces On "small geodesics" and free loop spaces

2008-06-03

arxiv.org/abs/0806.0637v1

Mathematics

Algebraic Topology

Scientific paper

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 \cite{Milnor} 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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