On the compactness problem for a family of generalized Seiberg-Witten equations in dimension three

Abstract

We prove an abstract compactness theorem for a family of generalized Seiberg-Witten equations in dimension three. This result recovers Taubes' compactness theorem for stable flat $\mathbf{P}{\mathrm{SL}}_2(\mathbf{C})$-connections as well as the compactness theorem for Seiberg-Witten equations with multiple spinors. Furthermore, this result implies a compactness theorem for the ADHM${}_{1,2}$ Seiberg-Witten equation, which partially verifies a conjecture by Doan and Walpuski.

accepted for publication in Duke Mathematical Journal

References in corpus (3)

• On counting associative submanifolds and Seiberg-Witten monopoles
• Deformation theory of the blown-up Seiberg-Witten equation in dimension three
• On the behavior of sequences of solutions to U(1) Seiberg-Witten systems in dimension 4