Mutation and gauge theory. I: Yang-Mills invariants (Q1969356)

If \(M\) is a 3-manifold containing an imbedded surface of genus 2, its mutant is obtained by cutting along the surface and gluing the pieces using a special involution on the surface. This paper shows that if \(M\) is an oriented homology 3-sphere then \(M\) and its mutant have the same Floer homology and the same \(Z\)-graded instanton homology of Fintushel-Stern. An analogous operation on 4-manifolds is shown to preserve the Donaldson polynomial invariant.