15 November 2021 On the compactness problem for a family of generalized Seiberg–Witten equations in dimension 3
Thomas Walpuski, Boyu Zhang
Author Affiliations +
Duke Math. J. 170(17): 3891-3934 (15 November 2021). DOI: 10.1215/00127094-2021-0005

Abstract

We prove an abstract compactness theorem for a family of generalized Seiberg–Witten equations in dimension 3. This result recovers Taubes’s compactness theorem for stable flat PSL2(C)-connections as well as the compactness theorem for Seiberg–Witten equations with multiple spinors by Haydys and Walpuski. Furthermore, this result implies a compactness theorem for the ADHM1,2 Seiberg–Witten equation, which partially verifies a conjecture by Doan and Walpuski.

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Thomas Walpuski. Boyu Zhang. "On the compactness problem for a family of generalized Seiberg–Witten equations in dimension 3." Duke Math. J. 170 (17) 3891 - 3934, 15 November 2021. https://doi.org/10.1215/00127094-2021-0005

Information

Received: 6 June 2019; Revised: 2 September 2020; Published: 15 November 2021
First available in Project Euclid: 18 November 2021

MathSciNet: MR4340726
zbMATH: 1500.53030
Digital Object Identifier: 10.1215/00127094-2021-0005

Subjects:
Primary: 53C07
Secondary: 35J70 , 57R57

Keywords: compactness , Gauge Theory , generalized Seiberg–Witten equations , geometric analysis

Rights: Copyright © 2021 Duke University Press

Vol.170 • No. 17 • 15 November 2021
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