On an invariant of plumbed homology 3-spheres

Abstract

The main purpose of this paper is to give some invariance property of a homology cobordism invariant of plumbed homology 3-spheres under a kind of blowing up process for auxiliary 4-V-manifolds. By using this property, we prove a homology cobordism invariance of an integral lift of the Rohlin invariant constructed by W. Neumann [6] and L. Siebenmann [12] in the set of all homology 3-spheres bounding plumbed 4-V-manifolds with $b_{2}^{+} + b_{2}^{-} \leq 2$ which are obtained by blowing down of smooth spin 4-manifolds.