I would like to study the Atiyah-Guillemin-Sternberg convexity theorem: proof and applications. I am already familiarised with hamiltonian actions, moment maps...and with elementary Morse theory. So my problem is to find a detailed proof of this theorem:
- What are the prerequisits: Morse-Bott functions, equivariant Darboux Theorem...?
- Is the original proof by Atiyah different from the Guillemin-Sternberg's proof?
- What is "the best reference" for a detailed treatment of this theorem?
Thanks for any help.