Smooth maps transverse to a foliation

Smooth Maps Transverse to a Foliation

Detecting When a Nonsingular Flow Is Transverse to a Foliation

We show that any foliation transverse to a C 1 nonsingular flow φ on a closed 3-manifold can be detected algorithmically. We use this to describe a procedure that, for any δ > 0, will determine whether or not there is a foliation whose tangent space is bounded away from the tangent space to φ by a distance of δ.

Transversality and Lefschetz Numbers for Foliation Maps

Let F be a smooth foliation on a closed Riemannian manifold M , and let Λ be a transverse invariant measure of F . Suppose that Λ is absolutely continuous with respect to the Lebesgue measure on smooth transversals. Then a topological definition of the Λ-Lefschetz number of any leaf preserving diffeomorphism (M,F) → (M,F) is given. For this purpose, standard results about smooth approximation a...

GROUPOID ASSOCIATED TO A SMOOTH MANIFOLD

‎In this paper‎, ‎we introduce the structure of a groupoid associated to a vector field‎ ‎on a smooth manifold‎. ‎We show that in the case of the $1$-dimensional manifolds‎, ‎our‎ ‎groupoid has a‎ ‎smooth structure such that makes it into a Lie groupoid‎. ‎Using this approach‎, ‎we associated to‎ ‎every vector field an equivalence‎ ‎relation on the Lie algebra of all vector fields on the smooth...

On Some Transverse Geometrical Structures of Lifted Foliation to Its Conormal Bundle

We consider the lift of a foliation to its conormal bundle and some transverse geometrical structures associated with this foliation are studied. We introduce a good vertical connection on the conormal bundle and, moreover, if the conormal bundle is endowed with a transversal Cartan metric, we obtain that the lifted foliation to its conormal bundle is a Riemannian one. Also, some transversally ...