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

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Langte Ma, Brandeis University
Fine Hall 314

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