We investigate the notion of the Casson-Seiberg-Witten invariant on integral homology S1×S3 introduced by Mrowka, Ruberman, and Saveliev in . 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 . 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.
|Commitee:||Huang, An, Mrowka, Tomasz Stanislaw|
|School Location:||United States -- Massachusetts|
|Source:||DAI-B 81/12(E), Dissertation Abstracts International|
|Keywords:||Casson invariant, End-periodic manifold, Fiber sum, Seiberg-Witten invariant, Torus surgery|
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