Free and based path groupoids

Ángel, Andrés; Colman, Hellen

doi:10.2140/agt.2023.23.1959

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Free and based path groupoids

Andrés Ángel and Hellen Colman

Algebraic & Geometric Topology 23 (2023) 1959–2008

DOI: 10.2140/agt.2023.23.1959

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 $X^{I}$ . 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.

Keywords

orbifolds, groupoids

Mathematical Subject Classification 2010

Primary: 18B40, 55P35, 58E40

Secondary: 55R91, 58D19

References

Publication

Received: 2 September 2017

Revised: 16 November 2021

Accepted: 22 February 2022

Published: 25 July 2023

Authors

Andrés Ángel
Departamento de Matemáticas Universidad de los Andes Bogota Colombia

Hellen Colman
Department of Mathematics Wright College Chicago, IL United States
https://www.hellencolman.com/math

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Volume 23, issue 5 (2023)