Topological Fundamental Groupoid. II. An action category of the fundamental groupoid

2023/05/08 by Holkar, Rohit Dilip, Hossain, Md Amir, Kulkarni, Dheeraj
#14H30 #22A22 #37C85 #57S #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.04668

Abstract

For a path connected, locally path connected and semilocally simply connected space X, let Π₁(X) denote its topologised fundamental groupoid as established in the first article of this series. Let E be the category of Π₁(X)-spaces in which the momentum maps are local homeomorphisms. We show that this category is isomorphic to that of covering spaces of X. Using this, we give different characterisations for free or proper actions of the fundamental groupoid in E.

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