Contents Online
Mathematical Research Letters
Volume 29 (2022)
Number 4
Fiber sum formulae for the Casson–Seiberg–Witten invariant of integral homology $S^1 \times S^3$
Pages: 1197 – 1227
DOI: https://dx.doi.org/10.4310/MRL.2022.v29.n4.a11
Author
Abstract
We prove the additivity of the Casson–Seiberg–Witten invariant of integral homology $S^1 \times S^3$ under fiber sum along embedded curves and embedded tori, which is the $4$‑dimensional analog of the additivity of the Casson invariant under connected-sum and splicing along knots. As an application, we compute the Casson–Seiberg–Witten invariant of a family of integral homology $S^1 \times S^3$ which arises as the mapping tori under maps of infinite order in the mapping class group of certain $3$‑manifolds.
Received 14 February 2020
Accepted 23 June 2020
Published 23 February 2023