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Title: The Casson invariant and applications
Authors: Bast, Mitch
Advisors: Szabó, Zoltán
Department: Mathematics
Class Year: 2020
Abstract: This paper familiarizes the reader with basic concepts and results in the topology of 3 and 4-manifolds before introducing the Rohlin invariant, a mod 2 invariant of oriented integral homology 3-spheres Y. The paper proceeds to introduce the Casson invariant as a signed count of irreducible SU(2) representations of the fundamental group of Y and contains proofs of its uniqueness, simple computational examples, a sketch of a proof of its existence, and generalization to the Casson-Walker invariant for rational homology 3-spheres. The paper concludes by highlighting the role played by the Casson invariant in a couple of applications: combinatorial triangulations of manifolds and the cosmetic surgery conjecture for 2-bridge knots.
Type of Material: Princeton University Senior Theses
Language: en
Appears in Collections:Mathematics, 1934-2020

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