Homology cobordism and classical knot invariants

Abstract

In this paper, we define and investigate Z 2 -homology cobordism invariants of Z 2homology 3-spheres which turn out to be related to classical invariants of knots. As an application, we show that many lens spaces have infinite order in the Z 2 -homology cobordism group and we prove a lower bound for the slice genus of a knot on which integral surgery yields a given Z 2 -homology sphere. We also give some new examples of 3-manifolds which cannot be obtained by integral surgery on a knot.