Minimal Nielsen Root Classes and Roots of Liftings

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.