[Binghamton Geometry/Topology Seminar] December 10

[Marco Varisco]

Binghamton Geometry/Topology Seminar
http://www.math.binghamton.edu/dept/topsem/

Date: Thursday, December 10, 2009

Time: 2:50 pm

Place: Library North 2205
(followed by coffee/tea in the Anderson Reading Room)

Speaker: Keith Jones

Title: Connectivity properties for actions on locally finite trees

Abstract: Let ρ be an action by a finitely generated group G on a
locally finite tree T. Viewing points of ∂T (the visual boundary of T)
as directions in T, we can use ρ to lift this sense of direction to G
and ask, for each end point E ∈ ∂T, whether G is “connected in the
direction of E”. If so, we say that ρ is controlled connected over E.
The Bieri-Geoghegan invariant Σ1(ρ) ⊆ ∂T consists of those points over
which ρ is controlled connected. This is a generalization of the
classical Bieri-Neumann-Strebel invariant.
In this talk, I will introduce a class of actions for which Σ1 can be
calculated by analyzing certain quotient maps between trees and show
that under reasonable hypotheses, Σ1 consists of no more than a single
point of ∂T for these actions. I will illustrate the result with some
examples.