Sequência espectral persistente de Leray e propriedades de separação para variedades generalizadas

Abstract

In this thesis we work on two different topics. On the one hand, we manage to construct a spectral sequence that calculates the persistent cohomology of a space from the persistent cohomology in each open and its interceptions of a covering that is the pre-image by a function of a covering of a known space. On the other hand, we achieved separation results by codimension-1 maps to generalized manifold. More specifically, we proved results that allow us to estimate the number of related components of the image complement of the map.