Elementary Abelian Group Actions on
Surfaces and the Geometry of Moduli Space
Indiana University Geometry Seminar
Abstract: The speaker and his co-author Aaron Wootton have recently completed a
topological classification of orientation preserving finite elementary abelian group actions on closed
surfaces. This is a first step in classifying all finite group actions on closed surfaces up to topological
equivalence, or alternatively, classifying all finite subgroups of the mapping class group up to conjugacy.
The latter problem is hopeless in general though many results are known (over a 100-year history), and,
using computer methods, a classification up to genus 50 or so is possible. The classification of
the finite subgroups of the mapping class group is essential to understanding the singularity structure
of moduli space, which serves as a geometric motivation for classification of the finite subgroups.
In this talk we will begin with an introduction to the classification of finite group actions on
surfaces, and its relation to the moduli space, via the finite subgroups of the mapping class group.
Then we give some detail on the classification results of the elementary abelian actions on surfaces.
Lecture and other materials
This page last updated on 9 Nov 07.