On Non-Abelian Symplectic Cutting
arXiv:1202.3077 · doi:10.1007/s00031-012-9202-9
Abstract
We discuss symplectic cutting for Hamiltonian actions of non-Abelian compact groups. By using a degeneration based on the Vinberg monoid we give, in good cases, a global quotient description of a surgery construction introduced by Woodward and Meinrenken, and show it can be interpreted in algebro-geometric terms. A key ingredient is the `universal cut' of the cotangent bundle of the group itself, which is identified with a moduli space of framed bundles on chains of projective lines recently introduced by the authors.
Various edits made, to appear in Transformation Groups. 28 pages, 8 figures
References in corpus (5)
- Hamiltonian group actions on symplectic Deligne-Mumford stacks and toric orbifolds
- Compactifications of reductive groups as moduli stacks of bundles
- Automorphisms of multiplicity free Hamiltonian manifolds
- Equivariant volumes of non-compact quotients and instanton counting
- Non-Abelian Cut Constructions and Hyperkähler Modifications