Mathematics

In 1981, Arnoux and Yoccoz constructed a pseudo-Anosov homeomorphism on a genus 3 surface that was the first known example of an odd degree pseudo-Anosov homeomorphism In 1985, David Fried constructed a pseudo-Anosov on a genus 3 surface with the same stretch factor by a completely different methods, and it has been unknown whether these maps are the same or distinct. I will be introducing these two maps and discussing some results that suggest that these are extremely likely to be the same map