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Free and based path groupoids

Andrés Ángel and Hellen Colman

Algebraic & Geometric Topology 23 (2023) 1959–2008
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.

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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