I will discuss the relationship between the geometry of a closed hyperbolic

3-manifold and the rank, or minimal number of generators, of its fundamental

group.  Specifically, I will describe a geometric decomposition of closed

 hyperbolic 3-manifolds with bounded rank and injectivity radius,

and indicate how to read off bounds for topological and geometric invariants

of the manifold, such as Heegaard genus and Cheeger constant.  Joint work 

with Juan Souto.