Delocalized L2-Invariants

We define extensions of the L2-analytic invariants of closed manifolds, called delocalized L2-invariants. These delocalized invariants are constructed in terms of a nontrivial conjugacy class of the fundamental group. We show that in many cases, they are topological in nature. We show that the marked length spectrum of an odd-dimensional hyperbolic manifold can be recovered from its delocalized L2-analytic torsion. There are technical convergence questions.