Root problem for convenient maps

Marcio Colombo Fenille, Oziride Manzoli Neto

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.

Keywords


Root problem; convenient map; mutation of homomorphism; symbolic mutation; system of equation on free group

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