Seminar

The mapping class group of a surface is the group of homotopy classes of homeomorphisms of the surface. This is an important group in mathematics because it connects to many, many fields of study, including algebraic geometry, low-dimensional topology, geometric group theory, hyperbolic geometry, representation theory, and number theory. One of the ways we understand the mapping class group is by understanding its action on a simplicial complex called the complex of curves. I’ll give an introduction to these objects, with emphasis on Thurston’s classification of elements of the mapping class group and Ivanov’s theorem that the group of automorphisms of the complex of curves is the mapping class group.