Topology & Geometric Group Theory Seminar

Fall 2011

1:30 – 2:30, Malott 203

Tuesday, November 1

Robert Bieri, University of Frankfurt and Binghamton University

Isolated and condensation points in the space of marked groups

This is joint work with Luc Guyot, Yves de Cornulier and Ralph Strebel.

The set G(m) of all isomorphism classes of m-generator groups can be identified with the set of all normal subgroups S of the free group F of rank m. G(m) is endowed with the Chabauty topology, which is based on the sets of all S containing one and avoiding a second given finite subset of F. It is a remarkable fact that whether a group G in G(m) is isolated or a condensation point, etc.… in this space is independent of its generating set and of m; hence those are group theoretic properties. I will present examples and condensation criteria, one of which is best understood in terms of the Geometric Invariant Σ(G) from joint work with Walter Neumann and Ralph Strebel.

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