Distinctness of two pseudo-Anosov maps
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913504962805760 |
|---|---|
| author | Schmidt, Thomas A. Walker, Mesa |
| author_facet | Schmidt, Thomas A. Walker, Mesa |
| contents | In 1981, Arnoux and Yoccoz gave the first examples of pseudo-Anosov maps with odd degree stretch factors. In 1985, D.~Fried deduced the existence of a pseudo-Anosov map in genus three with the same stretch factor as the Arnoux-Yoccoz example in that genus, and asked if these were the same. We show that they are distinct. We do this by, in a sense, reversing Fried's construction; we show that the mapping torus of the pseudo-Anosov map induced by the Arnoux-Yoccoz map on the surface obtained by blowing-up its two singularities has no cross section which is a torus with two points blown-up. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12803 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Distinctness of two pseudo-Anosov maps Schmidt, Thomas A. Walker, Mesa Dynamical Systems 57K20, 37E30 In 1981, Arnoux and Yoccoz gave the first examples of pseudo-Anosov maps with odd degree stretch factors. In 1985, D.~Fried deduced the existence of a pseudo-Anosov map in genus three with the same stretch factor as the Arnoux-Yoccoz example in that genus, and asked if these were the same. We show that they are distinct. We do this by, in a sense, reversing Fried's construction; we show that the mapping torus of the pseudo-Anosov map induced by the Arnoux-Yoccoz map on the surface obtained by blowing-up its two singularities has no cross section which is a torus with two points blown-up. |
| title | Distinctness of two pseudo-Anosov maps |
| topic | Dynamical Systems 57K20, 37E30 |
| url | https://arxiv.org/abs/2308.12803 |