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.

Abstract

Given a continuous map f:K→M from a 2-dimensional CW complex into a closed surface, the Nielsen root number N(f) and the minimal number of roots μ(f) of f satisfy N(f)≤μ(f). But, there is a number μC(f) associated to each Nielsen root class of f, and an important problem is to know when μ(f)=μC(f)N(f). In addition to investigate this problem, we determine a relationship between μ(f) and μ(f˜), when f˜ is a lifting of f 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.