18.937 - Topics in Geometric Topology - Spring 2006

D. Auroux - Mondays & Wednesdays, 9:30-11 in 2-136.

Lecture notes:

These handwritten notes are provided as is, without any guarantee of readability or accuracy.

Course description

This course will focus on braid groups, mapping class groups, and their applications to the topology of plane curves and complex surfaces.

The first half of the course will be mostly group-theoretic and loosely based on the book "Braids, Links, and Mapping Class Groups" by Joan Birman (Princeton University Press). It will cover the following topics:

The second half of the course will focus on applications to algebraic geometry (especially the study of plane curves and complex surfaces) and symplectic topology. We will in particular review Moishezon and Teicher's work on the braid monodromy of plane curves, as well as recent results on the topology of Lefschetz fibrations. The main topics will be: