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arxiv: math/0101159 · v1 · submitted 2001-01-18 · 🧮 math.SG · math.AG

Symplectic implosion

classification 🧮 math.SG math.AG
keywords implosionsymplecticcross-sectiongroupimplodedaffineassociatesbears
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Let $K$ be a compact Lie group. We introduce the process of symplectic implosion, which associates to every Hamiltonian $K$-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 $K$. We examine the nature of the singularities and describe in detail the imploded cross-section of the cotangent bundle of $K$, 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''.

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