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 -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 Seiberg–Witten equation, which partially verifies a conjecture by Doan and Walpuski.
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