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):
The following is a list of topics which I may attempt to cover in the course:
- 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
I will endeavor to provide a set of lecture notes online.
You may download them in dvi format or in
- Basic definitions
- Examples: word metrics, hyperbolic geometry, boundaries
- Ultrafilters, ultralimits, asymptotic cones
- 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