Alladi Ramakrishnan Hall

Topological fundamental groupoid

Md Amir Hossain

IMSc

There have been various notions of topologising the fundamental group or covering spaces. These topologies should also extend to fundamental groupoids. In this talk, we shall discuss two such topologies on the fundamental groupoid and prove that the fundamental groupoid is topological. We shall see that the fundamental groupoid of a topological group is a transformation groupoid. We shall discuss covering spaces as a natural action category of the fundamental groupoid. If time permits, we shall also discuss Haar system on the fundamental groupoid.