32nd Summer Conference on Topology and Its Applications
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.
Copyright © 2017, the Author
Lukina, Olga, "Classifying Matchbox Manifolds" (2017). Summer Conference on Topology and Its Applications. 38.