Trees and Group Actions Part I
Friday August 24, 2007
09:00AM - 09:50AM
Speakers:
Lisa Carbone
Abstract:
A tree is a non-empty connected graph without circuits. If a group G acts
on a tree X, certain machinery developed by Bass and Serre permits us to reconstruct the group G, the tree X, and the action of G on X, giving precise structure theorems for G and its subgroups. The Bass-Serre theory is a powerful combinatorial tool that has found wide applications in geometric group theory, discrete groups and lattices, infinite dimensional algebra, low dimensional topology and the construction of expanders. We will give an overview of the general methods of Bass and Serre, with emphasis on the following class of examples. When the tree X is homogeneous of degree q+1 with q a prime power, X is the Tits building of a rank 1 Lie group over non-archimedean local field,
or a rank 2 Kac-Moody group over a finite field. We indicate how to apply
the machinery of Bass and Serre to study these groups and the arithmetic
properties of their discrete subgroups.
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