Implosion, Contraction and Moore-Tachikawa

Abstract

We give a survey of the implosion construction, extending some of its aspects relating to hypertoric geometry from type $A$ to a general reductive group, and interpret it in the context of the Moore-Tachikawa category. We use these ideas to discuss how the contraction construction in symplectic geometry can be generalised to the hyperkähler or complex symplectic situation.

23 Pages. To appear in Int. J. Math. (special issue in honour of Oscar Garcia Prada)