Geometry and Topology Seminar

Presentations of periodic maps by Dehn twists

Susumu Hirose, Saga University

Details
Wednesday January 10, 2007  
  809 Physical Sciences Center
  4:00 pm / 3:45 tea  

Abstract Jakob Nielsen classified periodic maps on orientable surfaces by using homomorphisms from the fundamental group of the orbit space to the cyclic group ("valency data"). On the other hand, Max Dehn showed that any orientation-preserving homeomorphism is isotopic to a product of Dehn twists. Although these results are very classical, methods to get presentations of periodic maps by Dehn twists from "valency data" are still unknown, except for hyper-elliptic maps, for which there is a method due to Mizuho Ishizaka (Waseda University, Japan).

In this talk, I will introduce a method to get presentations for periodic maps by Dehn twists by using monodromies of plane curve singularities, especially A'Campo's "divide link".