Feuilletages et topologie spectrale

Abstract

Let \mathscr{F} be a codimension-one foliation, transversally oriented, of class C^r (r≥q 0) on a connected closed manifold M. The class of a leaf F of \mathscr{F} is defined to be the union of all leaves G with overline{F}=overline{G}. Let X be the space of classes of leaves in M and let X₀ be the union of open subsets of X which are homeomorphic to \bm{R} or to S¹. In this paper we prove that if the level of \mathscr{F} is well defined (in the sense of [{12}]), then X-X₀ is a spectral space.