Markov staircases

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Adaloglou, Nikolas, Brendel, Joé, Evans, Jonny, Hauber, Johannes, Schlenk, Felix
Natura: Preprint
Pubblicazione: 2025
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866909942455205888
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