Cornell Math - MATH 751, Fall 2003
MATH 751
Berstein Seminar in Topology
(Fall 2003)
Instructor: Kai-Uwe Bux
Following the tradition of the seminar, the students will be part of the decision about the topic. My suggestions are:
(a) Groups acting on trees and R-trees.
There is a lot of interesting material about this. Bass-Serre theory on groups acting on simplicial trees and relates to ways of splitting groups as free and amalgamated products. Group actions of R-trees often arise in unexpected ways for instance from measured laminations in surfaces
(b) Arithmetic and S-arithmetic groups.
Classical examples of arithmetic groups are SL_n(Z) or the group of upper triangular matrices with coefficients in Z. Replacing Z by so called S-arithmetic rings like Z[1/m], F_p[t], or F_p[t,1/t], one obtains S-arithmetic groups. In this case, the action of the group on associated buildings plays a crucial rule.