The stability of foliations of orientable 3-manifolds covered by a product

Shields, Sandra

doi:10.1090/S0002-9947-96-01631-5

The stability of foliations of orientable 3-manifolds covered by a product
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Trans. Amer. Math. Soc. 348 (1996), 4653-4671 Request permission

Abstract:

We examine the relationship between codimension one foliations that are covered by a trivial product of hyperplanes and the branched surfaces that can be constructed from them. We present a sufficient condition on a branched surface constructed from a foliation to guarantee that all $C^1$ perturbations of the foliation are covered by a trivial product of hyperplanes. We also show that a branched surface admits a strictly positive weight system if and only if it can be constructed from a fibration over $S^1$.

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