Manifolds that are not leaves of codimension one foliations

TL;DR

This paper introduces new examples of open manifolds that cannot be realized as leaves of any continuous codimension one foliation in a compact manifold, including simply connected manifolds with complex homotopy properties.

Contribution

It constructs specific open manifolds with complex topological features that are proven not to be leaves of any C^0 codimension one foliation.

Findings

Certain simply connected manifolds of dimension 5+ are not leaves of any C^0 codimension one foliation.

Manifolds with non-periodic homotopy or homology groups cannot be realized as leaves.

New classes of open manifolds are identified as non-leaves in foliation theory.

Abstract

We present new open manifolds that are not homeomorphic to leaves of any C^0 codimension one foliation of a compact manifold. Among them are simply connected manifolds of dimension 5 or greater that are non-periodic in homotopy or homology, namely in their 2-dimensional homotopy or homology groups.