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arXiv · 2604.17044

Deformation rigidity for Z/2 eigensections

Andriy Haydys·Siqi He·Willem Adriaan Salm
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Abstract

We prove a rigidity result for certain critical Z/2 eigensections of the Laplacian on S^2 associated to a flat real line bundle determined by a branch-point configuration. More precisely, we show that every minimal non-degenerate critical eigensection is deformation rigid: any sufficiently small deformation of the configuration that still admits a critical eigensection must come from an SO(3)-rotation. This generalizes the rigidity phenomenon previously discovered in symmetric examples of Taubes-Wu.

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Andriy Haydys, Siqi He, Willem Adriaan Salm. 2026-04-18. Deformation rigidity for Z/2 eigensections. https://arxiv.org/abs/2604.17044

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