2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77877We use noncommutative localization to construct a chain complex which counts the critical points of a circle-valued Morse function on a manifold, generalizing the Novikov complex. As a consequence we obtain new topological lower bounds on the minimum number of critical points of a circle-valued Morse function within a homotopy class, generalizing the Novikov inequalities.Differential GeometryAlgebraic Topologytext