Faithful Semitoric Systems

Abstract

This paper consists of two parts. The first provides a review of the basic properties of integrable and almost-toric systems, with a particular emphasis on the integral affine structure associated to an integrable system. The second part introduces faithful semitoric systems, a generalization of semitoric systems (introduced by Vu Ngoc and classified by Pelayo and Vu Ngoc) that provides the language to develop surgeries on almost-toric systems in dimension 4. We prove that faithful semitoric systems are natural building blocks of almost-toric systems. Moreover, we show that they enjoy many of the properties that their (proper) semitoric counterparts do.

References in corpus (7)

• Integrable systems, symmetries and quantization
• Symplectic quasi-states on the quadric surface and Lagrangian submanifolds
• Regular Poisson manifolds of compact types (PMCT 2)
• Vu Ngoc's Conjecture on focus-focus singular fibers with multiple pinched points
• Infinitely many monotone Lagrangian tori in del Pezzo surfaces
• Constructing integrable systems of semitoric type
• Smooth normal forms for integrable hamiltonian systems near a focus-focus singularity

Cited by in corpus (3)

• Integrable systems, symmetries and quantization
• Survey on recent developments in semitoric systems
• Asymptotic Lattices, Good Labellings, and the Rotation Number for Quantum Integrable Systems