Sobre o gênus de G-espaços e teoremas de coincidências

Abstract

Let G be a finite group acting freely in a Hausdorff paracompact topological space X and let Y be a k-dimensional metrizable space (or k-dimensional CW-complex). In this work, by using the genus of X; gen(X;G), we prove coincidence theorems for maps f : X ! Y . Such theorems generalize the main theorem proved by Aarts, Fokkink and Vermeer in [2]. Moreover, by using the Volovikov index defined in [39], we prove a Borsuk- Ulam theorem for compact Lie groups, which generalizes the main result proved by Biasi and Mattos in [7, 12].