EVENT DETAILS AND ABSTRACT

Title: Symmetries of laminations
Speaker: Olga Lukina
Speaker Info: University of Illinois at Chicago
Brief Description:
Special Note:
Abstract:

A lamination is a compact connected metrizable space which is locally homeomorphic to the product of a Euclidean disk and a Cantor set. A special class consists of laminations which are homeomorphic to the inverse limit of a sequence of finite-to-one coverings of a closed manifold. The transverse dynamics of such a lamination is given by an equicontinuous group action on a Cantor set.

In the talk, we will discuss the asymptotic discriminant, an algebraic invariant which classifies equicontinuous laminations up to return equivalence, recently introduced by the speaker in a joint work with Steven Hurder. We will give examples of actions on Cantor sets with non-trivial asymptotic discriminant, arising in various areas of dynamics, including arithmetic dynamics. We will also discuss the applications of the asymptotic discriminant to the classification of group actions on Cantor sets up to continuous orbit equivalence.