تقرير
Bounds for the number of moves between pants decompositions, and between triangulations
| العنوان: | Bounds for the number of moves between pants decompositions, and between triangulations |
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| المؤلفون: | Lackenby, Marc, Yazdi, Mehdi |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Geometric Topology, 57K20, 57K32 |
| الوصف: | Given two pants decompositions of a compact orientable surface $S$, we give an upper bound for their distance in the pants graph that depends logarithmically on their intersection number and polynomially on the Euler characteristic of $S$. As a consequence, we find an upper bound on the volume of the convex core of a maximal cusp (which is a hyperbolic structures on $S \times \mathbb{R}$ where given pants decompositions of the conformal boundary are pinched to annular cusps). As a further application, we give an upper bound for the Weil--Petersson distance between two points in the Teichm\"uller space of $S$ in terms of their corresponding short pants decompositions. Similarly, given two one-vertex triangulations of $S$, we give an upper bound for the number of flips and twist maps needed to convert one triangulation into the other. The proofs rely on using pre-triangulations, train tracks, and an algorithm of Agol, Hass, and Thurston. Comment: 43 pages, 12 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2401.14233 |
| رقم الأكسشن: | edsarx.2401.14233 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |