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

Aleksander Doan ^[1] ; Thomas Walpuski ^[2]
1. [1] Columbia University
  
  Columbia University
  
  Estados Unidos
2. [2] Michigan State University
  
  Michigan State University
  
  City of East Lansing, Estados Unidos
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 3, 2020
Idioma: inglés
DOI: 10.1007/s00029-020-00574-6
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Resumen
- 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.