## 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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