On non-Abelian symplectic cutting

Johan Martens*, Michael Thaddeus

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)1059-1084
Number of pages26
JournalTransformation Groups
Volume17
Issue number4
DOIs
Publication statusPublished - Dec 2012

Keywords

  • MANIFOLDS
  • DELIGNE-MUMFORD STACKS
  • KAHLER
  • VARIETIES
  • CONVEXITY PROPERTIES
  • CUTS
  • GEOMETRIC-QUANTIZATION
  • HAMILTONIAN TORUS ACTIONS
  • SURGERY
  • ORBIFOLDS

Fingerprint

Dive into the research topics of 'On non-Abelian symplectic cutting'. Together they form a unique fingerprint.

Cite this