2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77579It is shown that the Novikov inequalities for critical points of closed 1-forms hold with the von Neumann Betti numbers replacing the Novikov numbers. As a corollary we obtain a vanishing theorem for $L^2$ cohomology, generalizing a theorem of W. Lueck. We also prove that von Neumann Betti numbers coincide with the Novikov numbers for free abelian coverings.9 pagesDifferential GeometryMathematical PhysicsAlgebraic TopologyRepresentation TheorySymplectic Geometrytext