Deformation theory of the blown-up Seiberg-Witten equation in dimension three

Abstract

Associated with every quaternionic representation of a compact, connected Lie group there is a Seiberg-Witten equation in dimension three. The moduli spaces of solutions to these equations are typically non-compact. We construct Kuranishi models around boundary points of a partially compactified moduli space. The Haydys correspondence identifies such boundary points with Fueter sections - solutions of a non-linear Dirac equation - of the bundle of hyperkähler quotients associated with the quaternionic representation. We discuss when such a Fueter section can be deformed to a solution of the Seiberg-Witten equation.

v2: typos fixed, exposition improved

References in corpus (2)

• On counting associative submanifolds and Seiberg-Witten monopoles
• Nonlinear Dirac operator and quaternionic analysis

Cited by in corpus (3)

• On the compactness problem for a family of generalized Seiberg-Witten equations in dimension three
• A Gluing Theorem for the Kapustin-Witten Equations with a Nahm Pole
• Seiberg-Witten monopoles with multiple spinors on a surface times a circle