التفاصيل البيبلوغرافية
| العنوان: |
Large-scale geometry of the saddle connection graph |
| المؤلفون: |
Anja Randecker, Robert Tang, Valentina Disarlo, Huiping Pan |
| بيانات النشر: |
arXiv, 2020. |
| سنة النشر: |
2020 |
| مصطلحات موضوعية: |
Surface (mathematics), Gromov boundary, Applied Mathematics, General Mathematics, 010102 general mathematics, Scale (descriptive set theory), Geometric Topology (math.GT), 01 natural sciences, Tree (graph theory), Connection (mathematics), Combinatorics, Set (abstract data type), Mathematics - Geometric Topology, FOS: Mathematics, Graph (abstract data type), Mathematics - Combinatorics, Combinatorics (math.CO), 0101 mathematics, Saddle, Mathematics |
| الوصف: |
We prove that the saddle connection graph associated to any half-translation surface is 4-hyperbolic and uniformly quasi-isometric to the regular countably infinite-valent tree. Consequently, the saddle connection graph is not quasi-isometrically rigid. We also characterise its Gromov boundary as the set of straight foliations with no saddle connections. In our arguments, we give a generalisation of the unicorn paths in the arc graph which may be of independent interest.
Comment: 28 pages, 9 figures; v2: corrected statement of Corollary 1.3 (not affecting any other part of the paper) |
| DOI: |
10.48550/arxiv.2011.12975 |
| URL الوصول: |
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5b2725d3cae53df54ee6d7d9c489dc4a |
| Rights: |
OPEN |
| رقم الانضمام: |
edsair.doi.dedup.....5b2725d3cae53df54ee6d7d9c489dc4a |
| قاعدة البيانات: |
OpenAIRE |