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

Rohit Dilip Holkar; Md Amir Hossain; Dheeraj Kulkarni

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

Algebraic Topology 2023-05-09 v1

Authors: Rohit Dilip Holkar , Md Amir Hossain , Dheeraj Kulkarni

Abstract

For a path connected, locally path connected and semilocally simply connected space $X$ , let $\Pi_1(X)$ denote its topologised fundamental groupoid as established in the first article of this series. Let $\mathcal{E}$ be the category of $\Pi_1(X)$ -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 $\mathcal{E}$ .

Keywords

fundamental groupoid topological groupoid covering spaces action category local homeomorphisms

Cite

@article{arxiv.2305.04668,
  title  = {Topological Fundamental Groupoid. II. An action category of the fundamental groupoid},
  author = {Rohit Dilip Holkar and Md Amir Hossain and Dheeraj Kulkarni},
  journal= {arXiv preprint arXiv:2305.04668},
  year   = {2023}
}

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13 pages

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

Abstract

Keywords

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