In this work we exhibit examples of $5$-manifolds that are not homeomorphic to any leaf of any C² codimension one foliation of any compact $6$-manifold but are homeomorphic to (proper) leaves of some C¹ codimension one foliations and also to (proper) leaves of some Cⁱnf codimension $2$ foliations. The topology of these manifolds is characterized by Sturmian-like sequences.
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Carlos Meniño Cotón (2024) studied this question.
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