Abstract
We show that the following question, due to Haefliger can be answered positively for C1-foliations of codimenslon 2: if
is a foliation on a compact manifold with all leaves compact, does every neighborhood of any leaf F of
contain a neighborhood of F which is a union of leaves?
In the course of the proof we show that the Euler number of leaves which do not have the above property is zero for an open and dense subset of these leaves if the holonomy groups of these leaves are cyclic.
The answer to Haefliger's question in codimension 2 was first and independently obtained by Edwards-Millett-Sullivan [1]
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Vogt, E. Foliations of codimension 2 with all leaves compact. Manuscripta Math 18, 187–212 (1976). https://doi.org/10.1007/BF01184305
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DOI: https://doi.org/10.1007/BF01184305