Classification of Nahm pole solutions of the Kapustin-Witten equations on S¹× Σ× ℝ⁺

2019/01/02 by Siqi He, Rafe Mazzeo, He, Siqi +1
Mathematics · #53C07 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1901.00274

openalex publication_date 2019/01/02 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In this note, we classify all solutions to the SU(n) Kapustin-Witten equations on S¹×Σ× ℝ⁺, where Σ is a compact Riemann surface, with Nahm pole singularity at S¹×Σ× \0\. We provide a similar classification of solutions with generalized Nahm pole singularities along a simple divisor (a "knot") in S¹×Σ× \0\.

Related

• The ℝ invariant solutions to the Kapustin Witten equations on (0,∞) × ℝ² × ℝ with generalized Nahm pole asymptotics
• Energy bound for Kapustin-Witten solutions on S³×ℝ⁺
• Rotationally Invariant Singular Solutions to the Kapustin-Witten Equations
• Sequences of Nahm pole solutions to the SU(2) Kapustin-Witten equations
• The Expansions of the Nahm Pole Solutions to the Kapustin-Witten Equations