'22

36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

"Nonperiodic leaves of codimension one foliations"

Meniño Cotón, Carlos

It is known that a proper leaf of a $C^2$ codimension one foliation on a compact manifold belongs to one of the following two classes: leaves with periodic ends or leaves with infinitely many ends. It will be shown an example of a codimension one foliation of class $C^1$ that admits a proper, nonperiodic leaf with just two ends. This example can be improved in order to get a $5$-dimensional manifold that is not homeomorphic to any leaf of any $C^2$ codimension one foliation on any compact manifold but it can be realized as a leaf in a $C^1$ codimension one foliation. We remark that our method of construction only allows to produce nonperiodic leaves whose ends are almost periodic leaving open the non almost periodic case.

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