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

Rohit Dilip Holkar; Md Amir Hossain; Dheeraj Kulkarni

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arXiv · 2305.04668

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

Rohit Dilip Holkar·Md Amir Hossain·Dheeraj Kulkarni

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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 $\mathcal{E}$.

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BibTeX RIS

Rohit Dilip Holkar, Md Amir Hossain, Dheeraj Kulkarni. 2023-05-08. Topological Fundamental Groupoid. II. An action category of the fundamental groupoid. https://arxiv.org/abs/2305.04668

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