Non-Abelian Cut Constructions and Hyperkähler Modifications

Preprint number: CP3-Origins-2010-5
Authors: Andrew Dancer (Oxford) and Andrew Swann (CP3-Origins)
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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.