2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152190We define extensions of the $L^2$-analytic invariants of closed manifolds, called delocalized $L^2$-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 $L^2$-analytic torsion. There are technical convergence questions.22 pages, AMS-LatexDifferential Geometrytext