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arXiv · 1704.02954

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

Aleksander Doan·Thomas Walpuski
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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.

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Aleksander Doan, Thomas Walpuski. 2018-10-01. Deformation theory of the blown-up Seiberg-Witten equation in dimension three. https://doi.org/10.1007/s00029-020-00574-6

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