A relative Poincar\'e Theorem Jean-Paul Brasselet (Institut de Math\'ematiques de Luminy, France) This is a join work with Bernard Teissier. The origin of the work is a question by Fran\c cois Treves : Consider an analytic map $g:{\bf S }^n \to {\bf R}$ where ${\bf S}^n$ is the $n$-dimensional sphere, and a $r$-differential form $\omega$ of class ${\cal C}^{\infty}$ on ${\bf S}^n$ whose restriction to each non-singular fibre of $g$ is exact. Does there exist a H\"older $(r-1)$-differential form $H$ on ${\bf S}^n$ such that $dg \wedge (\omega - dH)=0$ ? Here $dH$ is considered as a distribution. We show the result in the more general situation of proper sub-analytic maps between non-singular spaces and for sub-analytic differential forms. The proof uses entertaining results in combinatorics and concerning Whitney forms. The lecture will be explicit and full of pictures.