低次元トポロジーセミナー


2018/6/19(Tue)

16:30--18:00 理学部 b棟 b342/346

Eriko Hironaka

AMS

Coxeter mapping classes and its generalizations

Coxeter mapping classes are mapping classes whose homological action is conjugate to a minimal essential element of a Coxeter system. By work of Smyth, McMullen and Leininger, classical pseudo-Anosov Coxeter mapping classes have dilatation bounded below by Lehmer’s number: 1.1762…. Recently, in joint work with L. Liechti, we showed that for alternating Coxeter mapping classes, a lower bound greater than one is also achieved, namely the square of the golden ratio. In this talk, we give a construction of generalized Coxeter mapping classes whose dilatations approach 1 asymptotically. These are examples of `Ferris wheel’ mapping classes.