Geometry, Topology and Dynamics Seminar
Steve Hurder
UIC
Homogeneous Matchbox Manifolds
Abstract: A "matchbox manifold" is a foliated space which is transversely modeled on a totally disconnected compact set.
Laminations in manifolds provide a classical example.
In this talk, I will discuss recent work with Alex Clark of the University of Leicester, UK,
in which we prove that a homogeneous matchbox manifold of any finite
dimension is homeomorphic to a McCord solenoid, thereby proving a
strong version of a conjecture of Fokkink and Oversteegen. The proof
uses techniques from the theory of foliations that involve making
important connections between homogeneity and equicontinuity. The
results provide a framework for the study of equicontinuous minimal
sets of foliations that have the structure of a matchbox manifold.
Monday September 28, 2009 at 3:00 PM in SEO 612