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Title: An Overview of the Casson Invariant
Authors: Talvola, Victoria
Advisors: Szabo, Zoltan
Department: Mathematics
Class Year: 2021
Abstract: In this thesis, I present an exposition on the Casson invariant, an invariant of integral homology 3-spheres. The thesis is intended for students who have studied basic topology: I cover the necessary background material on 3-manifolds and knots. This includes a definition of the Rokhlin invariant, which the Casson invariant generalizes. I describe the Casson invariant both axiomatically and through its explicit construction in terms of counting points in representation spaces of the fundamental group of a space. I also survey recent work on the Casson invariant, including generalizations such as the Casson-Walker invariant and applications to the cosmetic surgery conjecture.
Type of Material: Princeton University Senior Theses
Language: en
Appears in Collections:Mathematics, 1934-2021

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