Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 346519, 16 pages
Research Article

Minimal Nielsen Root Classes and Roots of Liftings

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

Received 24 April 2009; Accepted 26 May 2009

Academic Editor: Robert Brown

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 f:KM 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.