Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Avenida Trabalhador São-Carlense, 400 Centro Caixa Postal 668, 13560-970 São Carlos, SP, Brazil
Copyright © 2009 Marcio Colombo Fenille and Oziride Manzoli Neto. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Given a continuous map from a 2-dimensional CW complex into a closed surface, the Nielsen root number and the minimal number of roots of satisfy . But, there is a number associated to each Nielsen root class of and an important problem is to know when . In addition to investigate this problem, we determine a relationship between and , when is a lifting of through a covering space, and we find a connection between this problems, with which we answer several questions related to them when the range of the maps is the projective plane.