Symplectic implosion
Symplectic Geometry
2007-05-23 v1 Algebraic Geometry
Abstract
Let be a compact Lie group. We introduce the process of symplectic implosion, which associates to every Hamiltonian -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 . We examine the nature of the singularities and describe in detail the imploded cross-section of the cotangent bundle of , 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''.
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