Nonperiodic leaves of codimension one foliations

Abstract

In this work we exhibit examples of $5$-manifolds that are not homeomorphic to any leaf of any $C^2$ codimension one foliation of any compact $6$-manifold but are homeomorphic to (proper) leaves of some $C^1$ codimension one foliations and also to (proper) leaves of some $C^\inf$ codimension $2$ foliations. As far as we know, this is the first example of this nature. In addition, it is shown examples of $C^r$ codimension one foliations, $r\in [0,2)$, with a minimal invariant set whose leaves are pairwise nonhomeomorphic.

16 pages, 2 figures

Cited by in corpus (1)

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