Transversely Cantor laminations as inverse limits

Abstract

Abstract. We demonstrate that any minimal transversely Cantor compact lamination of dimension p and class C 1 without holonomy is an inverse limit of compact branched manifolds of dimension p. To prove this result, we extend the triangulation theorem for C 1 manifolds to transversely Cantor C 1 laminations. In fact, we give a simple proof of this classical theorem based on the existence of C 1 -compatible differentiable structures of class C ∞ .

Untitled

“…A matchbox manifold X is equicontinuous if and only if it is a solenoid [Clark and Hurder 2013, Theorem 7.9]; and X is homogeneous if and only if it is a McCord solenoid [Clark and Hurder 2013, Theorem 1.1]; this is the case where it is a G-foliated space. See [Alcalde Cuesta et al 2011] for a generalization using inverse limits of compact branched manifolds.…”

Lectures on Foliation Dynamics

“…Assume there are given orientation-preserving, smooth, proper covering maps P = {p : B → B −1 | > 0}. Then the inverse limit topological space (8) S P ≡ lim ← − {p :…”