| Abstract: |
| Almost-toric systems are important in mirror symmetry. We give a classification of $4$-dimensional compact almost-toric systems up to fiber-preserving symplecctomorphisms. This generalizes the classification by Pelayo--V\~u Ng\d{o}c on simple semitoric systems and that by the speaker together with Pelayo and Palmer on semitoric systems, both in dimension four. The extra difficulty for almost-toric systems is the lack of a global circle action. The polygon invariant is replaced by an almost-toric closed disk, and we give appropriate notions of focus-focus label and twisting indices in the almost-toric case. |
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