Questions tagged [foliations]

This tag is for questions about foliations in differential geometry and use in conjunction with the tag (differential geometry).

A foliation of a smooth manifold is a particular decomposition into connected, injectively immersed submanifolds and, these submanifolds are called the leaves of the foliation. If all of these leaves are equidimensional then the foliation is called regular or, otherwise it is called a singular foliation. According to the Frobenius theorem, a regular foliation on a smooth manifold can be equivalently expressed as an integrable distribution on the tangent bundle.

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What is the leaf space of the Kronecker foliation of the torus?

The leaves of the Kronecker foliation of the torus are diffeomorphic to the real line $\mathbb{R}$ and are dense on $T^2$. I cannot, however, describe what is the leaf space $T^2/\mathcal{F}$.
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Complete Stability Theorem

I am studying Geometrical Theory of Foliations, more specifically: the Complete Stability Theorem, which says: If $\text{Cod}(\mathscr{F}) = 1$, $M$ is an compact and connected manifold, and there is a compact leaf with finite fundamental group, so…
Allain JF
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