2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76852We define and study the signature, A-hat genus and higher signatures of the quotient space of an $S^1$-action on a closed oriented manifold. We give applications to questions of positive scalar curvature and to an Equivariant Novikov Conjecture.35 pages, Theorem 2 addedDifferential Geometrytext