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 $H{F}^{+}(Y;\mathfrak{s})$. In 2005, Némethi 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 Némethi's conjecture.

8 pages, comments welcome!