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Moment maps and Morse functions

  1. Jan 16, 2016 #1

    Ssnow

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    It is know that let ##M## a compact symplectic manifold with ##G=T^{d_{T}}## a torus of dimension ##d_{T}## acting on ##M## in Hamiltonian fashion with Moment map ##\Phi:M\rightarrow \mathfrak{t}^{*}##, then ##\Phi^{\xi}=\langle \Phi(m),\xi\rangle## is a Morse function in each of its component (for ##\xi\in\mathfrak{t}##). What I want to discuss here is what happen if we consider now the product group ##P=G\times T^{d_{T}}## where ##G## is a Lie group of dimension ##d_{G}##, assuming that ##P## acts in Hamiltonian way and that at each point of ##M## the moment map of ##G## is ##\Phi_{G}(m)=0\in \mathfrak{g}^{*}##. It is ##\Phi_{P}## a Morse function?
     
  2. jcsd
  3. Jan 21, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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