2010/02/09 by Andrew Dancer, Andrew Swann, Dancer, Andrew +1
Mathematics · #53C26 #53D20 #57S25 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:53C26 #msc:53D20 #msc:57S25
paper · pdf · doi:10.48550/arxiv.1002.1837
16 pages
arxiv created 2010/02/09 · openalex publication_date 2010/02/09 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.