# Symplectic implosion

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Lisa Jeffrey, University of Toronto

Symplectic implosion was developed to solve the problem that the symplectic cross-section of a Hamiltonian K-space is usually not symplectic, when K is a compact Lie group. The symplectic implosion is a stratified symplectic space, introduced in a 2002 paper of the speaker with Guillemin and Sjamaar.  I survey some examples showing how symplectic implosion has been used. I describe the universal imploded cross-section, which is the imploded cross-section of the cotangent bundle of a compact Lie group. Imploded cross-sections are normally not smooth manifolds. We describe some invariants (for example intersection homology) which replace homology  for singular stratified spaces. (Joint work with Sina Zabanfahm)