Tesis
Classes características de variedades topológicas e generalizadas
Date
2022-03-24Registration in:
Author
Barbosa, Alex Melges
Institutions
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.