Generating mapping class groups with two elements

Geometry Topology Student Seminar
Wednesday, February 1, 2017 - 14:05
1 hour (actually 50 minutes)
Skiles 006
Georgia Tech
Wajnryb showed that the mapping class group of a surface can be generated by two elements, each given as a product of Dehn twists. We will discuss a follow-up paper by Korkmaz, "Generating the surface mapping class group by two elements." Korkmaz shows that one of the generators may be taken to be a single Dehn twist instead. He then uses his construction to further prove the striking fact that the two generators can be taken to be periodic elements, each of order 4g+2, where g is the genus of the surface.