*Ma 192b* - Stable commutator length

### Instructor: Danny Calegari

### Lectures Tu-Th 1-2:30pm in 257 Sloan

### Description of course:

In this course we present and discuss some elements of the geometric
theory of 2-dimensional (bounded) homology from several points of
view, making contact with low-dimensional geometry and topology, and
with group dynamics. We start off at an elementary level, but we
hope to present some original results which will also be of interest
to the experts, and to outline a number of open problems which might
make good thesis topics. There are few prerequisites for the class, since
much of the material will be presented from scratch. Students should
know about the topology of surfaces, some of the details of a first
course in algebraic topology, and perhaps some hyperbolic geometry
(though this will not be necessary if the student is prepared to take
a couple of things on faith). Roughly, the plan of the course is:

- Introduction
- Bavard's duality theorem
- Hyperbolicity and spectral gaps
- Free and surface groups
- Groups with few quasimorphisms
- Statistical properties

The textbook for the course is my lecture notes
scl.

### References:

- Bavard, C.
*Longueur stable des commutateurs* Enseign.
Math. (2) **37** (1991), no. 1-2, 109-150
- Calegari, D. arXiv papers math/0605354, 0802.1352, 0803.4137, 0805.1755,
0807.0395