We prove that a homogeneous matchbox manifold is homeomorphic to a McCord solenoid,
thereby proving a strong version of a conjecture of Fokkink and Oversteegen, which is a …

In this paper we find smooth embeddings of solenoids in smooth foliations. We show that if a
smooth foliation F of a manifold M contains a compact leaf L with H 1 (L; R) not equal to 0 …

We show that an n-dimensional compactum X embeds in R^ m, where m> 3 (n+ 1)/2, if and
only if X x X-\Delta admits an equivariant map to S^{m-1}. In particular, X embeds in R^{2n} …

The study of foliation dynamics seeks to understand the asymptotic properties of leaves of
foliated manifolds, their statistical properties such as orbit growth rates and geometric …

A matchbox manifold is a connected, compact foliated space with totally disconnected
transversals; or in other notation, a generalized lamination. It is said to be Lipschitz if there …

This survey is based on a series of five lectures, given May 3--7, 2010, at the Centre de
Recerca Matematica, Barcelona. The goal of the lectures was to present aspects of the …

For a generic degree d smooth map f: N n→ M n we introduce its “transverse fundamental
group” π (f), which reduces to π 1 (M) in the case where f is a covering, and in general …

We study the Hausdorff and the box dimensions of closed invariant subsets of the space of
pointed trees, equipped with a pseudogroup action. This pseudogroup dynamical system …

A foliated space M of dimension n is a continuum which has a local product structure: every
point x∈ M has an open neighborhood Ux⊂ M homeomorphic to an open subset Ux⊂ Rn …

The limit topological space S is a lamination [7], with foliation FS having leaves of dimension
n. The initial manifold L0 is called the base of the solenoid S, and each covering pl+ 1: Ll+ …