$\Delta$ Invariants of Plumbed Manifolds

Shimal Harichurn; András Némethi; Josef Svoboda

doi:10.3842/sigma.2025.091

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arXiv · 2412.02042

$\Delta$ Invariants of Plumbed Manifolds

Shimal Harichurn·András Némethi·Josef Svoboda

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Abstract

We study the minimal $q$-exponent $\Delta$ in the BPS $q$-series $\widehat{Z}$ of negative definite plumbed 3-manifolds equipped with a spin$^{\rm c}$-structure. We express $\Delta$ of Seifert manifolds in terms of an invariant commonly used in singularity theory. We provide several examples illustrating the interesting behaviour of $\Delta$ for non-Seifert manifolds. Finally, we compare $\Delta$ invariants with correction terms in Heegaard-Floer homology.

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Shimal Harichurn, András Némethi, Josef Svoboda. 2024-12-02. $\Delta$ Invariants of Plumbed Manifolds. https://doi.org/10.3842/sigma.2025.091

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