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arXiv · 2308.12803

Distinctness of two pseudo-Anosov maps

Thomas A. Schmidt·Mesa Walker
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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.

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Thomas A. Schmidt, Mesa Walker. 2024-09-17. Distinctness of two pseudo-Anosov maps. https://arxiv.org/abs/2308.12803

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