A slice theorem for singular Riemannian foliations, with applications

Abstract

We prove a slice theorem around closed leaves in a singular Riemannian foliation, and we use it to study the C ∞ C^\infty -algebra of smooth basic functions, generalizing to the inhomogeneous setting a number of results by G. Schwarz. In particular, in the infinitesimal case we show that this algebra is generated by a finite number of polynomials.