Comparison of Lasso and Whisker topologies on fundamental groupoids and local triviality

Pakdaman, Ali

doi:10.22103/jmmr.2025.24987.1776

Comparison of Lasso and Whisker topologies on fundamental groupoids and local triviality

Document Type : Research Paper

Author

Ali Pakdaman

Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran

10.22103/jmmr.2025.24987.1776

Abstract

‎This paper is devoted to comparing the Lasso topology and the Whisker topology on the fundamental groupoid. We prove that for locally path connected and semilocally simply connected spaces, the two topologies coincide. However, the converse does not hold in general, and we provide a partial converse. Furthermore, we observe that the topological fundamental groupoid is not étale, and we show that the topological fundamental groupoids of locally path connected and semilocally simply connected spaces, equipped with these topologies, are locally trivial. Through several examples, we illustrate the necessity of these conditions

Keywords

Topological fundamental groupoid‎

‎Locally trivial groupoid‎

‎Lasso topology‎

‎Whisker topology

Subjects

Geometry and Topology

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