"Pseudo-Anosov constructions by Arnoux-Yoccoz and Fried" by Mesa Walker from Oregon State University.
Abstract: In the 1970s, Thurston investigated self-maps of surfaces and introduced a classification. He called some of these self maps pseudo-Anosov homeomorphisms (pA), and associated to each an algebraic integer, called its stretch factor. Examples of pA with stretch factors of even algebraic degree were easily found. It was not until 1981 that Arnoux and Yoccoz constructed the first example of a pA with an odd degree stretch factor. By completely different methods, in 1985, David Fried deduced the existence of a pA on the same topological surface and with the same stretch factor. It has remained an open question if these are the same pA. I will introduce these two maps and discuss results showing that Fried’s arguments can be applied to the Arnoux-Yoccoz pA to find an associated toral map, and indicate how I intend to complete the proof that the two maps in question are in fact the same.
Monday, November 28 at 12:00pm to 12:50pm
Kidder Hall, 237
2000 SW Campus Way, Corvallis, OR 97331