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Gluing and Surgery For Casson-Seiberg-Witten Invariant of Integral Homology S^1脳S^3

Topology Seminar

Gluing and Surgery For Casson-Seiberg-Witten Invariant of Integral Homology S^1脳S^3

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Langte Ma, Brandeis University

Given an integral homology S1脳S3, the Casson-Seiberg-Witten听invariant 位SW听was introduced by Mrowka-Ruberman-Saveliev as a 4-dimensional听analogue of Casson鈥檚 invariant. In this talk I will discuss how 位SW听changes under听topological operations corresponding to the formulae of Casson鈥檚 invariant听under surgery, connected-summing, and knot-splicing. In the end, I will present听examples illustrating how embedded tori arise naturally in some integral homology听S1脳S3.