Authors derive a closed-form formula for Gompf's θ-invariant of canonical contact structures on Seifert fibered 3-manifolds and a recursive formula for general plumbing trees using Legendrian surgery descriptions.
The Heegaard Floer d-invariant for more rational homology spheres
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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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math.GT 1years
2026 1verdicts
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The Gompf $\theta$-Invariant of Canonical Contact Structures via Legendrian Surgery
Authors derive a closed-form formula for Gompf's θ-invariant of canonical contact structures on Seifert fibered 3-manifolds and a recursive formula for general plumbing trees using Legendrian surgery descriptions.