Tuesday, April 27
Keith Jones, Binghamton University
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, Σ1(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 Σ1(ρ), where ρ is an action of G by isometries on a proper CAT(0) space M. This Σ1(ρ) is a subset of the boundary-at-infinity of M. Their theorems extend some of the well-known properties of Σ1(G) (where, in the older case, ρ is the above translation action.)
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