Extending regular foliations

Smith, J. W.

Annales de l'Institut Fourier, Tome 19 (1969) no. 2, pp. 155-168.

On dit qu’une structure feuilletée $F$ de dimension $p$ sur une variété différentiable $M$ se prolonge s’il existe une structure feuilletée $F^{\prime }$ de dimension $p+1$ sur $M$ telle que $F\subset F^{\prime }$. Le résultat principal de cet article est que $F$ se prolonge sur les ensembles relativement compacts de $M$ sous les hypothèses que $M$ et $F$ soient orientables, que $F$ soit propre et que la classe d’Euler de $M/F$ s’annule.

A $p$-dimensional foliation $F$ on a differentiable manifold $M$ is said to extend provided there exists a $(p+1)$-dimensional foliation $F^{\prime }$ on $M$ with $F\subset F^{\prime }$. Our main result asserts that if $M$ and $F$ extends over relatively compact subsets of $M$.

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