Surgery and Excision for Furuta-Ohta invariants on Homology $S^1\times S^3$

Abstract

We prove a surgery formula and an excision formula for the Furuta-Ohta invariant ${\lambda }_{FO}$ defined on homology $S^1\times S^3$, which provides more evidence on its equivalence with the Casson-Seiberg-Witten invariant ${\lambda }_{SW}$. These formulae are applied to compute ${\lambda }_{FO}$ of certain families of manifolds obtained as mapping tori under diffeomorphisms of $3$-manifolds. In the course of the proof, we give a complete description of the degree-zero moduli space of ASD instantons on $4$-manifolds of homology $H_{\ast }(D^2\times T^2;\mathbb{Z})$ with a cylindrical end modeled on $[0,\infty )\times T^3$.

Added sections that discuss holonomy perturbations and regularity issues. The argument for the existence of the asymptotic map is rewritten more carefully with more details

References in corpus (1)

• On the monopole Lefschetz number of finite order diffeomorphisms