On Non-Abelian Symplectic Cutting

Details On Non-Abelian Symplectic Cutting On Non-Abelian Symplectic Cutting

2012-02-14

arxiv.org/abs/1202.3077v1

Mathematics

Symplectic Geometry

25 pages, 7 figures

Scientific paper

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.

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