Nicola Cavallucci

Finiteness theorems and collapsing of CAT(0) spaces and groups

Finiteness theorems for certain classes of metric spaces with geometric bounds are known since Cheeger's finiteness theorem for manifolds. I will present a result obtained in a joint work with A.Sambusetti (Rome) stating that there are at most a finite number of uniformly packed, geodesically complete, CAT(0) spaces admitting a uniformly cocompact discrete subgroup of isometries, up to homotopy equivalence.