Análise em variedades topológicas

Abstract

This dissertation consists of a detailed study on a series of results published in the last ten years on maps between topological manifolds, with focus in the so called homological version of the famous inverse and implicit mapping theorem. With an approach which in- volves differential and homological techniques, we present a version of the inverse mapping theorem for differential maps which are not necessarily continuously differentiable. As a consequence, we improve the known differential version of the implicit mapping theorem and we present an existence and uniqueness theorem for certain differential equations.