11/06/2013, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
Daniele Sepe, Centro de Análise Matemática, Geometria e Sistemas Dinâmicos
From semi-toric systems to Hamiltonian $S^1$-spaces
Semi-toric integrable systems on closed four dimensional manifolds, introduced by Vu Ngoc, lie at the intersection of integrable Hamiltonian systems and Hamiltonian torus actions. In particular, they are integrable Hamiltonian systems which have one integral that generates an effective Hamiltonian $S^1$-action. Vu Ngoc showed that these systems share an important property with symplectic toric manifolds, i.e. it is possible to associate a family of convex polygons to each of them. On the other hand, considering the manifold only with the Hamiltonian $S^1$-action, they give rise to examples of Hamiltonian $S^1$-spaces, which have been classified by Karshon. The aim of this talk is to illustrate how, given a semi-toric system, Karshon's invariants of the underlying Hamiltonian $S^1$-space can be reconstructed from one (and hence any) convex polygon associated to the system. Time permitting, we will consider how to construct examples of these systems starting from symplectic toric manifolds.
This is joint work with Sonja Hohloch and Silvia Sabatini.
