Conjuntos minimais de pontos fixos e coincidências de aplicações fibradas

Abstract

This thesis was developed in two parts. Firstly, we consider a pair of fiber-preserving maps f1, f2 : M → M in a fiber bundle with base S1 and fiber Klein bottle. Using an algebraic system of equations we found in what situations the minimal coincidence set over S1 of the pair (f1, f2) is empty. In the second part, motivated by this problem, we consider a fiber-preserving map f : M → M in a fiber bundle with base S1 and fiber torus. Using the one-parameter fixed point theory we studied the minimal fixed point set over S1 of the map f. In some fiber bundle we classified completely this sets.