Algebra and Topology Seminar

4pm Tuesday 02 November 2004
Udo Baumgartner
University of Newcastle

A space `at infinity' for totally disconnected, locally compact groups

I will outline the construction of a complete metric space of `directions' which describes the asymptotic behavior of automorphisms of totally disconnected, locally compact groups under iteration. This `space of directions' admits an isometric action by the group and recovers familiar objects such as the set of ends of the tree for the group of inner automorphisms of the group of isometries of a regular locally finite tree; and the spherical Bruhat-Tits building for the group of inner automorphisms of the set of rational points of a semisimple group over a local field.

The space of directions lends itself best to the analysis of isometry groups of locally finite CAT(0) cell complexes. We are currently trying to understand several examples of (non-linear) simple totally disconnected, locally compact groups in that class constructed by Paulin/Haglund and Rémy in terms of their topological invariants, among them the space of directions. If time permits, I will sketch the partial knowledge we gained so far.

This is joint work with George Willis.




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