Non-Abelian Cut Constructions and Hyperkähler Modifications

Abstract

We discuss a general framework for cutting constructions and reinterpret in this setting the work on non-Abelian symplectic cuts by Weitsman. We then introduce two analogous non-Abelian modification constructions for hyperkähler manifolds: one modifies the topology significantly, the other gives metric deformations. We highlight ways in which the geometry of moment maps for non-Abelian hyperkähler actions differs from the Abelian case and from the non-Abelian symplectic case.

16 pages

References in corpus (1)

• A hyperkahler structure on the cotangent bundle of a complex Lie group

Cited by in corpus (1)

• On Non-Abelian Symplectic Cutting