Root problem for convenient maps

Abstract

In this paper we study when the minimal number of roots of the so-called convenient maps from two-dimensional CW complexes into closed surfaces is zero. We present several necessary and sufficient conditions for such a map to be root free. Among these conditions we have the existence of specific liftings for the homomorphism induced by the map on the fundamental groups, existence of the so-called mutation of a specific homomorphism also induced by the map, and existence of particular solutions of specific systems of equations on free groups over specific subgroups.