English

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

Differential Geometry 2022-02-02 v2

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 PSL2(C)\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 ADHM1,2_{1,2} Seiberg-Witten equation, which partially verifies a conjecture by Doan and Walpuski.

Keywords

Cite

@article{arxiv.1904.03749,
  title  = {On the compactness problem for a family of generalized Seiberg-Witten equations in dimension three},
  author = {Thomas Walpuski and Boyu Zhang},
  journal= {arXiv preprint arXiv:1904.03749},
  year   = {2022}
}

Comments

accepted for publication in Duke Mathematical Journal