Generic intersections of differentiable submanifolds

Abstract

Consider a transitive action of a Lie group $G$ on a (real analytic) manifold $M$ of dimension $m$, and two (embedded) submanifolds $A$ and $B$ in $M$ of sufficiently large class and of dimension $k$ and $l$, respectively. We prove that, for a generic $\sigma \in G$, the intersection $\sigma (A)\cap B$ is transversal, whence a submanifold of dimension $k+l-m$ or the empty set. This paper is a continuation of our previous article, devoted to definable transitive actions of definable groups on manifolds and generic intersections in an o-minimal structure, and inspired by a question of Jan Mycielski about the intersections of translates of analytic sets in the real plane.

This paper has been withdrawn by the author because it can be easily obtained from the parametric transversality theorem