Classifying foliations of 3-manifolds via branched surfaces

摘要

We use branched surfaces to define an equivalence relation on C~1 codimension one foliations of any closed orientable 3-manifold that are transverse to some fixed nonsingular flow. There is a discrete metric on the set of equivalence classes with the property that foliations that are sufficiently close (up to equivalence) share important topological properties.