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Mathematics > Differential Geometry

arXiv:1805.02773 (math)
[Submitted on 7 May 2018 (v1), last revised 26 Mar 2022 (this version, v2)]

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

Authors:Clifford Henry Taubes
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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.
Comments: Some typos corrected and some arguments simplified in this version
Subjects: Differential Geometry (math.DG); Geometric Topology (math.GT)
MSC classes: 53C07, 57R57
Cite as: arXiv:1805.02773 [math.DG]
  (or arXiv:1805.02773v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1805.02773

Submission history

From: Clifford H. Taubes [view email]
[v1] Mon, 7 May 2018 22:49:05 UTC (2,507 KB)
[v2] Sat, 26 Mar 2022 17:01:20 UTC (8,409 KB)
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