The Heegaard Floer d-invariant for more rational homology spheres

Abstract

The Heegaard Floer d-invariant for a rational homology sphere Y and spin$^c$-structure $\mathfrak{s}$ is defined as the minimal absolute grading of a generator of $HF^+(Y; \mathfrak{s})$. In 2005, N\'emethi used lattice homology to compute the d-invariant for a particular class of negative-definite plumbed rational homology spheres, and conjectured that his formula should hold for all negative-definite plumbed rational homology spheres. In this paper, we use Zemke's isomorphism between lattice and Heegaard Floer homology to prove N\'emethi's conjecture.