Regularização de pares de folheações contínuas e transversais em variedades bidimensionais compactas

Abstract

Let M be a compact manifold, two-dimensional, differentiable of class C and (F, G) be a pair of class C0 of orientable foliations on M. Suppose that F and G has the same and totally disconnected closed subset S as singularities, and that F and G are transversal in M S. Under these conditions we prove that there is a pair (F, G) of class C1 that is topologically equivalent to the pair (F, G). Moreover, we prove that the following conditions are equivalent: (A) any minimal set of F and G are trivial. (B) F and G are topologically equivalent to C2 foliations F and G. (C) F and G are topologically equivalent to to C foliations F and G.