Dissertation/Thesis Abstract

Gluing and Surgery for the Casson-Seiberg-Witten Invariant of Integral Homology S1 × S3
by Ma, Langte, Ph.D., Brandeis University, 2020, 198; 27833826
Abstract (Summary)

We investigate the notion of the Casson-Seiberg-Witten invariant on integral homology S1×S3 introduced by Mrowka, Ruberman, and Saveliev in [36]. We prove a torus surgery formula for the invariant as an extension of the product formula for Seiberg-Witten invariants on manifolds with b+ > 0. We also prove formulae of this invariant corresponding to fiber sums along tori and simple closed curves respectively. As an application, we obtain a formula for this invariant on mapping tori of 3-manifolds under finite-order diffeomorphisms whose fixed-point sets consist of simple closed curves, which was conjectured by Lin, Ruberman, and Saveliev in [27]. In the course of the proof for these formulae, we give a complete description of the structure of the Seiberg-Witten moduli space over manifolds of homology as H*(D2×T2) with a cylindrical end modeled on [0, ∞)×T3.

Indexing (document details)
Advisor: Ruberman, Daniel
Commitee: Huang, An, Mrowka, Tomasz Stanislaw
School: Brandeis University
Department: Mathematics
School Location: United States -- Massachusetts
Source: DAI-B 81/12(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Casson invariant, End-periodic manifold, Fiber sum, Seiberg-Witten invariant, Torus surgery
Publication Number: 27833826
ISBN: 9798645472047
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