An inequality for the h-invariant in instanton Floer theory

Details An inequality for the h-invariant in instanton Floer theory An inequality for the h-invariant in instanton Floer theory

2001-11-04

arxiv.org/abs/math/0111038v3

Mathematics

Differential Geometry

35 pages. One section has been added outlining the proof of the main theorem, and one appendix has been added. To appear in To

Scientific paper

In math.DG/9903083 (henceforth referred to as EA) we defined an integer invariant $h(Y)$ for oriented integral homology 3-spheres $Y$ which only depends on the rational homology cobordism class of $Y$ and is additive under connected sums. In this paper we establish lower bounds for $h(Y)$ when $Y$ is the boundary of a smooth, compact, oriented 4-manifold with $b_2^+=1$. As applications, we give an upper bound for how much $h$ changes under -1 surgery on knots in terms of the slice genus of the knot, and compute $h$ for a family of Brieskorn spheres. This paper contains, in revised form, most of the material from v1 of EA that was left out in the final version of that paper. In particular, Theorem 1 of the present paper is virtually the same as Theorem 1 of v1 of EA. The proof is also essentially the same, but the exposition has been improved, with more details.

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