Maximal Hamiltonian tori for polygon spaces. (Q1417741)

Let \(M\) be a symplectic manifold and let \(S(M)\) be the group of symplectomorphisms of \(M\). A sub-torus of \(S(M)\) is called a symplectic torus. These tori are partially ordered by inclusions. In this paper, the authors study the maximal symplectic tori of polygon spaces with a particular emphasis on bending tori. Since polygon spaces are simply connected, symplectic tori act on \(M\) in a Hamiltonian fashion. The authors determine some maximal elements and give examples where maximal Hamiltonian tori are not all of the same dimension.