Seifert-Van Kampen Theorem and Representation of Covering Spaces

Chatterjee, Annoy (2025) Seifert-Van Kampen Theorem and Representation of Covering Spaces. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Annoy Chatterjee (22MP005)) 22MP005_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (687kB)

Abstract

We explore fundamental theorems in algebraic topology, following Hatcher's Algebraic Topology for the most part. We start with trying to understand some basic de�nitions and concepts in category theory and move onto de�ning the fundamental groupoid and the fundamental groups of topological spaces. We then move onto one of the main theorems in this report: the Seifert-Van Kampen Theorem. We study its proof in details and see an example. Finally, we go on to the other main topic in the book: the construction of arbitrary covers by action of the fundamental groups on �bres of covering maps and as we result we get some kind of "representation" of the covering spaces.

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