A note on open 3-manifolds supporting foliations by planes

Details A note on open 3-manifolds supporting foliations by planes A note on open 3-manifolds supporting foliations by planes

2009-05-27

arxiv.org/abs/0905.4526v1

Mathematics

Geometric Topology

Scientific paper

We show that if $N$, an open connected $n$-manifold with finitely generated fundamental group, is $C^{2}$ foliated by closed planes, then $\pi_{1}(N)$ is a free group. This implies that if $\pi_{1}(N)$ has an Abelian subgroup of rank greater than one, then $\mathcal{F}$ has at least a non closed leaf. Next, we show that if $N$ is three dimensional with fundamental group abelian of rank greater than one, then $N$ is homeomorphic to $\mathbb{T}^2\times \mathbb{R}.$ Furthermore, in this case we give a complete description of the foliation.

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