Return to Colloquia & Seminar listing
Van Kampen's embedding obstruction for discrete groups
Colloquium| Speaker: | Mladen Bestvina, University of Utah |
| Location: | 693 Kerr |
| Start time: | Mon, Oct 21 2002, 4:10PM |
Description
I will start by recalling the work of van Kampen and his
method of proving that e.g. the "utilities graph" does not embed in the
plane (plus the higher-dimensional analogs).
I will then give a lower bound to the dimension of a contractible
manifold on which a given group can act properly discontinuously. In
particular, the $n$-fold product of nonabelian free groups cannot act
properly discontinuously on $R^{2n-1}$. The idea is to find a utility
graph (or an analog) "at infinity of the group". If there is time, I
will discuss why SL_n(Z) cannot act properly discontinuously on a
contractible manifold whose dimension is less than the dimension of the
symmetric space SL_n(R)/SO_n.