Universal torsion, L^2-invariants, polytopes and the Thurston norm

We introduce universal torsion which is defined for $L^2$-acyclic manifolds with torsion free fundamental group and takes values in certain $K_1$-groups of a skew field associated to the integral group ring. It encompasses well-know invariants such as the Alexander polynomial and $L^2$-torsion. We discuss also twisted $L^2$-torsion and higher order Alexander polynomials which can also be derived from the universal invariant and assign certain polytopes to the universal torsion. This gives especially in dimension 3 interesting invariants which recover for instance the Thurston norm.