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January  2015, 35(1): 247-281. doi: 10.3934/dcds.2015.35.247

From compact semi-toric systems to Hamiltonian $S^1$-spaces

 1 Section de Mathématiques, EPFL, SB MATHGEOM CAG, Station 8, 1015 Lausanne, Switzerland 2 CAMGSD, Instituto Superior Técnico, Av. Rovisco Pais, Lisboa, 1049-001, Portugal 3 Instituto de Matemática, Universidade Federal Fluminense, Rua Mário Santos Braga, 24020-240 Niteroi, RJ, Brazil

Received  December 2013 Revised  March 2014 Published  August 2014

We show how any labeled convex polygon associated to a compact semi-toric system, as defined by Vũ ngọc, determines Karshon's labeled directed graph which classifies the underlying Hamiltonian $S^1$-space up to isomorphism. Then we characterize adaptable compact semi-toric systems, i.e. those whose underlying Hamiltonian $S^1$-action can be extended to an effective Hamiltonian $\mathbb{T}^2$-action, as those which have at least one associated convex polygon which satisfies the Delzant condition.
Citation: Sonja Hohloch, Silvia Sabatini, Daniele Sepe. From compact semi-toric systems to Hamiltonian $S^1$-spaces. Discrete & Continuous Dynamical Systems - A, 2015, 35 (1) : 247-281. doi: 10.3934/dcds.2015.35.247
References:

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