Simplicial volume of open manifolds

The simplicial volume is a proper homotopy invariant of manifolds introduced by Gromov in the 80's. In the first part of the thesis, I prove that the only open contractible 3-manifold with vanishing simplicial volume is the Euclidean space, and that any other open contractible 3-manifold has infinite simplicial volume. With the same techniques, I compute the spectrum of simplicial volume of open irreducible 3-manifolds. This work is contained in a paper joint with Prof. Roberto Frigerio. In the second part, I prove that (under some technical hypotheses) an open manifold with amenable fundamental group at infinity has finite simplicial volume. I prove that the same conclusion holds for manifolds which are simply connected at infinity.