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

Sonja Hohloch; Silvia Sabatini; Daniele Sepe

doi:10.3934/dcds.2015.35.247

Article Contents

2015, Volume 35, Issue 1: 247-281. Doi: 10.3934/dcds.2015.35.247

This issue Previous Article Self-trapping and Josephson tunneling solutions to the nonlinear Schrödinger / Gross-Pitaevskii equation Next Article Conformal metrics on $\mathbb{R}^{2m}$ with constant Q-curvature, prescribed volume and asymptotic behavior

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

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

Received: November 30, 2013

Revised: February 28, 2014

Published: December 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 37J05, 37J35, 53D20.

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