Sequences of Nahm pole solutions to the SU(2) Kapustin-Witten equations

2018/05/07 by Clifford Henry Taubes, Taubes, Clifford Henry · 3 citations
Mathematics · #53C07 #57R57 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1805.02773

openalex publication_date 2018/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper describes the behavior of sequences of solutions to the Kapustin-Witten equations with Nahm pole asymptotics on the product of the half-line with a compact, oriented, Riemannian 3-manifold. These sequences have sub-sequences that either converge to another solution after acting term-wise by an automorphism of the principle bundle, or they converge after renormalization to a (weak) Z/2 harmonic 1-form from the 3-manifold; it is independent of the half-line coordinate in the product structure.

Citations

• The zero loci of Z/2 harmonic spinors in dimension 2, 3 and 4
• Energy bound for Kapustin-Witten solutions on S³×ℝ⁺

Cited by

• Perturbation and Pruning of Nondegenerate ℤ/2 Harmonic 1-forms
• Search for Z/2 eigenfunctions on the sphere using machine learning
• The Expansions of the Nahm Pole Solutions to the Kapustin-Witten Equations

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