Nonperiodic leaves of codimension one foliations

2024/04/16 by Cotón, Carlos Meniño
#37C86 #57R30 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2404.10485

Abstract

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. 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∈[0,2), with a minimal invariant set whose leaves are pairwise nonhomeomorphic.

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