## Topology & Geometric Group Theory Seminar

## Spring 2010

### 1:30 – 2:30, Malott 203

Tuesday, April 27

**Keith
Jones**, Binghamton University

*
Connectivity properties for groups acting on locally finite trees
*

With any finitely generated group G there is associated a canonical
translation action of G on the vector space V := G ⊗_{
Z} **R**. The Bieri-Neumann-Strebel invariant,
Σ^{1}(G), is a subset of the sphere at infinity of V.
It measures the directions in V over which Cayley graphs of G are
connected. Bieri and Geoghegan generalized this invariant to
Σ^{1}(ρ), where ρ is an action of G by
isometries on a proper CAT(0) space M. This
Σ^{1}(ρ) is a subset of the boundary-at-infinity of
M. Their theorems extend some of the well-known properties of
Σ^{1}(G) (where, in the older case, ρ is the above
translation action.)

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