English

Symplectic implosion

Symplectic Geometry 2007-05-23 v1 Algebraic Geometry

Abstract

Let KK be a compact Lie group. We introduce the process of symplectic implosion, which associates to every Hamiltonian KK-manifold a stratified space called the imploded cross-section. It bears a resemblance to symplectic reduction, but instead of quotienting by the entire group, it cuts the symmetries down to a maximal torus of KK. We examine the nature of the singularities and describe in detail the imploded cross-section of the cotangent bundle of KK, which turns out to be identical to an affine variety studied by Gelfand, Vinberg, Popov, and others. Finally we show that ``quantization commutes with implosion''.

Keywords

Cite

@article{arxiv.math/0101159,
  title  = {Symplectic implosion},
  author = {Victor Guillemin and Lisa Jeffrey and Reyer Sjamaar},
  journal= {arXiv preprint arXiv:math/0101159},
  year   = {2007}
}

Comments

30 pages, LaTeX 2e