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arXiv · 2410.08175

A note on the symplectic classification of almost-toric systems

Xiudi Tang
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Abstract

Since simple semitoric systems were classified about fifteen years ago, and semitoric systems five years ago, we want to move a step forward to almost-toric systems. We give a classification of compact almost-toric systems in dimension four up to fiber-preserving symplectomorphisms, in terms of the base, Taylor series, and twisting indices, analogous to the five invariants for semitoric systems. For convenience, we specify an ordering of focus-focus values and a choice of two cut rays at each of them.

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Xiudi Tang. 2024-10-10. A note on the symplectic classification of almost-toric systems. https://arxiv.org/abs/2410.08175

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