*Stable commutator length* - An introduction to 2-dimensional
bounded cohomology; 2007

### Instructor: Danny Calegari

### Lectures Monday 13:20-14:50 in W832

### 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 a very elementary level, but we
hope to present some original results which will also be of interest
to the experts. There are very few prerequisites for the class, since
most 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
- Spectral gaps
- Rationality
- Statistical properties

### References:

- Bavard, C.
*Longueur stable des commutateurs* Enseign.
Math. (2) **37** (1991), no. 1-2, 109-150