English

Distinctness of two pseudo-Anosov maps

Dynamical Systems 2024-09-19 v2

Abstract

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.

Keywords

Cite

@article{arxiv.2308.12803,
  title  = {Distinctness of two pseudo-Anosov maps},
  author = {Thomas A. Schmidt and Mesa Walker},
  journal= {arXiv preprint arXiv:2308.12803},
  year   = {2024}
}

Comments

19 pages, 9 figures; Updated version has more detailed background, further comments