Homology 3-spheres bounding acyclic 4-manifolds

Abstract

Let Σ(a1 ,a 2 ,... , an) be a Seifert fibered homology 3-sphere with a1 even. We show that if µ(Σ(a1 ,a 2 ,... , an)) = 1 mod 2, then the class of Σ(a1 ,a 2 ,... , an) has infinite order in the homology cobordism groupof homol- ogy 3-spheres. In the proof we use Seiberg-Witten's monopole equation on four- dimensional V-manifolds.