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Free and based path groupoids

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Ángel,  Andrés
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Ángel, A., & Colman, H. (2023). Free and based path groupoids. Algebraic & Geometric Topology, 23(5), 1959-2008. doi:10.2140/agt.2023.23.1959.


Cite as: https://hdl.handle.net/21.11116/0000-000D-ACDA-C
Abstract
We give an explicit description of the free path and loop groupoids in the Morita
bicategory of translation topological groupoids. We prove that the free path groupoid
of a discrete group acting properly on a topological space X is a translation groupoid
given by the same group acting on the topological path space XI . We give a detailed
description of based path and loop groupoids and show that both are equivalent to
topological spaces. We also establish the notion of homotopy and fibration in this
context.