A note on laminations with symmetric leaves

TL;DR

This paper demonstrates that, except in dimension 4, certain Riemannian solenoidal laminations with symmetric leaves are topologically equivalent to inverse limits of finite covers of compact locally-symmetric manifolds.

Contribution

It establishes a topological classification of laminations with symmetric leaves as inverse limits of finite covers, extending understanding of their structure beyond dimension 4.

Findings

Laminations with symmetric leaves are homeomorphic to inverse limits of finite covers.

The classification holds for all dimensions except four.

Provides a new perspective on the topology of solenoidal laminations.

Abstract

We prove that (apart from dimension $n=4$), each Riemannian solenoidal lamination with transitive homeomorphism group and leaves isometric to a symmetric space $X$ of noncompact type, is homeomorphic to the inverse limit of the system of finite covers of a compact locally-symmetric $n$-manifold.