The fundamental groupoid as a topological space
Автор: Utrecht Geometry Centre
Загружено: 2022-03-02
Просмотров: 1766
Описание:
This is a video for the course Topologie en Meetkunde taught in Utrecht University.
Given a space X, we topologise its fundamental groupoid. We then observe that, as long as X is sufficiently nice, the universal cover of X is a subspace of the fundamental groupoid.
We illustrate these results in the particular case of the circle.
Website of the Utrecht Geometry Centre: http://utrechtgeometrycentre.nl/
Lecturer: Álvaro del Pino (https://alvarodelpino.com/)
00:00 Statement of the results
04:41 Discussion about local simply-connectedness
07:17 The fundamental groupoid of S1: identities
08:14 The fundamental groupoid of S1: source fibres
11:42 The fundamental groupoid of S1 is homeomorphic to the cylinder
13:03 The fundamental groupoid of S1: target fibres
14:27 The fundamental groupoid of S1: opens
15:54 Summary
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