Mutation and Gauge Theory I: Yang-Mills Invariants

Details Mutation and Gauge Theory I: Yang-Mills Invariants Mutation and Gauge Theory I: Yang-Mills Invariants

1997-10-29

arxiv.org/abs/dg-ga/9710034v1

Mathematics

Differential Geometry

AMSLaTeX, 24 pages, 2 figures

Scientific paper

Mutation 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.

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