Some open problems about mapping class groups of surfaces |
Abstract: This talk will be about the many ways that group-theoretic structure in the mapping class group of a surface goes hand-in-hand with geometric structure in the topology of 3-manifolds. It will focus on the most recent evidence of this dichotomy, a measure of the complexity of an element in the mapping class group that was introduced by John Hempel in 2002. It is known as the "distance" of a Heegaard splitting. |