[Binghamton Geometry/Topology Seminar] December 2

[Lucas Sabalka]

                  BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

Date:  Thursday, December 2, 2010
Time:  2:50-3:50pm
Place:  Library North 2205 followed by coffee/tea in the Anderson
         Reading Room.

Speaker:  Robert Bieri
Title:  Horospherical limit sets of modules over groups on CAT(0)-spaces

Abstract:  (See http://www.math.binghamton.edu/dept/topsem/index.html if
your email client does not display this abstract correctly)  This is a
report on joint work with Ross Geoghegan. I will emphasize the classical
background, which is the notion of the limit set Λ(Γ) of a discrete group Γ
of Moebius transformations on the Riemann sphere Ĉ as introduced by Henri
Poincaré in 1882.
Poincaré Extension allows one to interpret Λ(Γ) as the limit set of Γ acting
by isometries on the unit ball model of hyperbolic 3-space M, with ∂M = Ĉ.
We modify, generalize and refine this as follows: The modification is that
we use the horospherical limit set L(Γ) which is a subset of the classical
limit set Λ(Γ); the generalization is that we do this for an arbitrary group
Γ acting on any proper CAT(0) space M; and the refinement is that we study
not only the full set L(Γ) but have a functorial way to attach to every
finitely generated Γ-module A characteristic subsets Σ( M; A ) and °Σ( M; A
) of L(Γ), which are particularly interesting when L(Γ) = ∂M.
Our investigations have led us to extend the category of Γ-modules by
introducing morphisms between Γ-modules (called Γ-finitary homomorphisms)
which are more general and hence more flexible than Γ-homomorphisms but
still share some of their coarse features. We feel that they are of
independent interest as some basic techniques of homological algebra carry
over to the Γ-finitary module category.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://www1.math.binghamton.edu/pipermail/topsem/attachments/20101129/1163a360/attachment.html