The Heegaard Floer d-invariant for more rational homology spheres

Isabella Khan

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arXiv · 2605.05332

The Heegaard Floer d-invariant for more rational homology spheres

Isabella Khan

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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.

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Isabella Khan. 2026-05-06. The Heegaard Floer d-invariant for more rational homology spheres. https://arxiv.org/abs/2605.05332

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