Title

Classifying Matchbox Manifolds

Author(s)

Olga Lukina, University of Illinois at ChicagoFollow

Document Type

Semi-plenary Lecture

Publication Date

6-2017

Publication Source

32nd Summer Conference on Topology and Its Applications

Abstract

A matchbox manifold is a compact connected foliated space, locally homeomorphic to the product of a Euclidean disk and a Cantor set. Strange attractors in dynamical systems, and exceptional minimal sets of smooth foliations present examples of matchbox manifolds. Many actions of profinite groups on trees can be suspended to obtain matchbox manifolds, and similar examples arise in other contexts and in other parts of mathematics.

Thus there is a natural problem of classifying matchbox manifolds. The most tractable class of matchbox manifolds is the class of weak solenoids which are the inverse limits of finite-to-one coverings of closed manifolds. In my talk, I will describe the recent results in this direction, obtained by my co-authors and myself. This includes the asymptotic discriminant, an algebraic invariant which can be seen as the measure of local complexity of matchbox manifolds.

Comments

This document is available for download with the permission of the presenting author and the organizers of the conference. Permission documentation is on file.

Copyright

Copyright © 2017, the Author

eCommons Citation

Lukina, Olga, "Classifying Matchbox Manifolds" (2017). Summer Conference on Topology and Its Applications. 38.
https://ecommons.udayton.edu/topology_conf/38