## Math 597F, Spring 2002

This is the home page for Math 597F, * Topics in Coarse Geometry. *
Our goal in this course is to understand by way of examples some of the
structure `at infinity' that can be carried by a metric (or, more generally, a
`coarse') space. The connection between coarse geometry and operator algebras
will be mentioned, but it isn't the central subject of the course; we'll
concentrate on geometry and coarse topology for its own sake.
The course meets in 308 Boucke at 11:15 on Mondays, Wednesdays, and Fridays.

There is no course textbook. However, the following books are interesting
(certainly) and relevant (possibly):

- Bridson and Haefliger,
* Metric Spaces of Non-Positive Curvature *
- Ghys and de la Harpe,
* Les Groupes Hyperboliques d'apres Mikhael Gromov
*
- The complete works of the aforementioned Mikhael Gromov, especially
*
Asymptotic Invariants of Infinite Groups * and * Metric Structures for
Riemannian and Non-Riemannian Spaces *
- Mostow,
* Strong Rigidity for Locally Symmetric Spaces *

The following is a list of topics which I may attempt to cover in the course:
- Basic definitions
- Examples: word metrics, hyperbolic geometry, boundaries
- Ultrafilters, ultralimits, asymptotic cones
- Amenability
- Mostow rigidity (easy case)
- Gromov hyperbolicity, homological consequences, Mineyev's remetrization
theorem, Bonk-Schramm embedding theorem
- Finite asymptotic dimension; Dranishnikov's embedding theorem
- Property A, embeddability in Hilbert space, expanders
- The groupoid of a coarse structure

I will endeavor to provide a set of lecture notes online.
You may download them in dvi format or in
pdf format.