Invariance de la Gamma-dimension pour certaines familles k\"ahl\'eriennes de dimension 3

In this article, we study some properties of deformation invariance of the Gamma-dimension (defined for X a compact k"ahler manifold). This birational invariant is defined as the codimension of the maximal compact subvarieties in the universal cover of X. In the surface case, the deformation invariance is a straightforward consequence of a theorem of Y.-T. Siu. Using some results from F. Campana et Q. Zhang, we settle this invariance for certain type of K"ahler families of dimension 3.