Curve complexes and mapping class groups

Geometry Topology Working Seminar
Friday, September 3, 2010 - 1:00pm
2 hours
Skiles 114
Georgia Tech
The mapping class group is the group of symmetries of a surface (modulo homotopy).  One way to study the mapping class group of a surface S is to understand its action on the set of simple closed curves in S (up to homotopy).  The set of homotopy classes of simple closed curves can be organized into a simplicial complex called the complex of curves.  This complex has some amazing features, and we will use it to prove a variety of theorems about the mapping class group.  We will also state some open questions.  This talk will be accessible to second year graduate students.