Every 3-Manifold Admits a Transverse Pair of Codimension One Foliations Which Cannot be Raised to a Total Foliation
Atsushi Sato · Advanced studies in pure mathematics · 2018
IntroductionLet M be an n-dimensional C~ manifold with or without boundary and let .fFbe a CT foliation of codimension k of M (r> I).If 8M=I=0.then for each connected component (8M)t of 8M, each leaf of §" is assumed to be transverse to (8M)t, that is,• T,,? + T,,8M = T"M, x e (8M)£> or assumed to be tangent to (8M)t, that is, T",$' c T,,8M, x e (8M)" where T,,$' denotes the tangent space of $' at x.In the former case, the restriction of $' to (8M)" $'i(8M),={L n (8M)t; L e $'}