2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33378Mutation is an operation on 3-manifolds containing an embedded surface of genus 2. It is defined by cutting along the surface and regluing using the `hyperelliptic' involution, and is known to preserve many 3-manifold invariants. I show that mutation of a homology 3-sphere preserves its (instanton) Floer homology, and that a related operation on 4-manifolds preserves the Donaldson invariants. A companion article (in preparation) will treat invariants based on the Seiberg-Witten equations.AMSLaTeX, 24 pages, 2 figuresDifferential GeometryGeometric TopologyQuantum Algebratext