Feuilletages et topologie spectrale

Abstract

Let $\mathcal{F}$ be a codimension-one foliation, transversally oriented, of class $C^r(r\ge 0)$ on a connected closed manifold $M$. The class of a leaf $F$ of $\mathcal{F}$ 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 $X_0$ be the union of open subsets of $X$ which are homeomorphic to $R$ or to $S^1$. In this paper we prove that if the level of $\mathcal{F}$ is well defined (in the sense of [12]), then $X-X_0$ is a spectral space.