English

$\Delta$ Invariants of Plumbed Manifolds

Geometric Topology 2025-10-28 v2

Abstract

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

Keywords

Cite

@article{arxiv.2412.02042,
  title  = {$\Delta$ Invariants of Plumbed Manifolds},
  author = {Shimal Harichurn and András Némethi and Josef Svoboda},
  journal= {arXiv preprint arXiv:2412.02042},
  year   = {2025}
}