Dottorato in MATEMATICA

Titolo della tesi: Finiteness and rigidity of hyperbolizable manifolds

(please wait for an updated version) we study the free subgroups of the fundamental group of hyperbolizable manifolds with bounded entropy. In the cocompact case, we find an entropy-systolic ineqaulity and an entropy cardinality inequality. As a consequence we deduce a topological finiteness theorem for compact hyperbolizable manifolds of bounded entropy and diameter, and in dimension 3 a differential rigidity theorem for hyperbolizable manifolds within the class of compact, orientable, manifolds with torsionless fundamental group and bounded entropy and diameter.