Topological canal foliations

抄録

Regular canal surfaces of ℝ³ or 𝕊³ admit foliations by circles: the characteristic circles of the envelope. In order to build a foliation of 𝕊³ with leaves being canal surfaces, one has to relax the condition “canal” a little (“weak canal condition”) in order to accept isolated umbilics. Here, we define a topological condition which generalizes this “weak canal” condition imposed on leaves, and classify the foliations of compact orientable 3-manifolds we can obtain this way.