  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.
