Non-Abelian Cut Constructions and Hyperkähler Modifications

Details Non-Abelian Cut Constructions and Hyperkähler Modifications Non-Abelian Cut Constructions and Hyperkähler Modifications

2010-02-09

arxiv.org/abs/1002.1837v1

Mathematics

Differential Geometry

16 pages

Scientific paper

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 hyperk\"ahler manifolds: one modifies the topology significantly, the other gives metric deformations. We highlight ways in which the geometry of moment maps for non-Abelian hyperk\"ahler actions differs from the Abelian case and from the non-Abelian symplectic case.

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