Chennai Mathematical Institute

Seminars




3:30 pm, Seminar Hall
Commuting conjugates of finite-order mapping classes

Kashyap Rajeevsarathy
IISER, Bhopal.
20-03-19


Abstract

Let $\m$ be the mapping class group of the closed orientable surface $S_g$ of genus $g\geq 2$. In this talk, we state conditions under which two finite-order mapping classes will have commuting conjugates in $\m$. As an application, we show that any finite-order mapping class, whose corresponding orbifold is not a sphere, has a conjugate that is liftable under a finite cyclic cover. Furthermore, we show that any torsion element in the centralizer of an irreducible finite order mapping class is of order at most $2$. We also give conditions for the primitivity of certain torsion elements of $\m$. Finally, we describe some realizations of two-generator finite abelian groups of $\m$ as hyperbolic isometry groups.