# Two Distinct Pseudo-Anosov Maps of Odd Degree

# Two Distinct Pseudo-Anosov Maps of Odd Degree

Start:

Tuesday, December 5, 2023 10:00 am

Location:

WNGR 201

Mesa Walker

Oregon State University

In 1981, Arnoux and Yoccoz constructed the first known family of odd degree pseudo-Anosov homeomorphisms. In 1985, David Fried constructed another family of pseudo-Anosov homemorphisms using completely different methods: studying cross sections of the mapping torus of a toral automorphism with periodic orbits blown up. Fried’s genus 3 homeomorphism and Arnoux and Yoccoz’s genus 3 homeomorphism both have the same stretch factor, and Fried asked if these maps are distinct or the same. We show that these maps are in fact distinct by showing that the mapping torus of Arnoux and Yoccoz’s pseudo-Anosov homeomorphism does not have Fried’s blown up torus as a cross section.

Contact:

Holly Swisher