Moment Maps and Combinatorial Invariants of Hamiltonian Tn-spaces
Victor W. Guillemin
Gebundenes Buch

Moment Maps and Combinatorial Invariants of Hamiltonian Tn-spaces

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The action of a compact Lie group, G, on a compact sympletic manifold gives rise to some remarkable combinatorial invariants. The simplest and most interesting of these is the moment polytope, a convex polyhedron which sits inside the dual of the Lie algebra of G. One of the main goals of this monograph is to describe what kinds of geometric information are encoded in this polytope. For instance, the first chapter is largely devoted to the Delzant theorem, which says that there is a one-one correspondence between certain types of moment polytopes and certain types of symplectic G-spaces. (One ...