Markov staircases
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866909942455205888 |
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| author | Adaloglou, Nikolas Brendel, Joé Evans, Jonny Hauber, Johannes Schlenk, Felix |
| author_facet | Adaloglou, Nikolas Brendel, Joé Evans, Jonny Hauber, Johannes Schlenk, Felix |
| contents | Rational homology ellipsoids are certain Liouville domains diffeomorphic to rational homology balls and having Lagrangian pin-wheels as their skeleta. From the point of view of almost toric fibrations, they are a natural generalisation of usual symplectic ellipsoids. We study symplectic embeddings of rational homology ellipsoids into the complex projective plane and we show that for each Markov triple, this problem gives rise to an infinite staircase. A key ingredient in the proof is the result that any two such embeddings are Hamiltonian isotopic. We also prove constraints on sizes for pairs of disjoint embeddings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03224 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Markov staircases Adaloglou, Nikolas Brendel, Joé Evans, Jonny Hauber, Johannes Schlenk, Felix Symplectic Geometry Algebraic Geometry Differential Geometry Geometric Topology 53D35 Rational homology ellipsoids are certain Liouville domains diffeomorphic to rational homology balls and having Lagrangian pin-wheels as their skeleta. From the point of view of almost toric fibrations, they are a natural generalisation of usual symplectic ellipsoids. We study symplectic embeddings of rational homology ellipsoids into the complex projective plane and we show that for each Markov triple, this problem gives rise to an infinite staircase. A key ingredient in the proof is the result that any two such embeddings are Hamiltonian isotopic. We also prove constraints on sizes for pairs of disjoint embeddings. |
| title | Markov staircases |
| topic | Symplectic Geometry Algebraic Geometry Differential Geometry Geometric Topology 53D35 |
| url | https://arxiv.org/abs/2509.03224 |