Classes características de variedades topológicas e generalizadas

Abstract

In this work, we will initially present generalized bundles, a concept developed by Fadell with the objective of generalizing vector bundles, Stiefel-Whitney classes andWu’s formula from the context of smooth manifolds to topological manifolds. After that, we will use the generalized bundles to obtain original results of Thom, Stiefel-Whitney,Wu and Euler classes of topological manifolds, as well as present a second proof of Wu’s formula for topological manifolds and the topological version of the Poincaré-Hopf theorem. Finally, we will use the Poincaré and Poincaré-Lefschetz dualities to more comprehensively construct the Stiefel-Whitney classes of generalized manifolds in order to present, for the first time in the literature, a proof of the Wu’s formula for such manifolds.