On algebraic extensions and decomposition of morphisms in free groups

Noam Kolodner

Published 2019-06-29Version 1

We give a counterexample to a conjecture by Miasnikov, Ventura and Weil, stating that an extension of free groups is algebraic if and only if the corresponding morphism of their core graphs are onto, for every basis of the ambient group. In the course of the proof we present a partition of the set of homomorphisms between free groups that may be of independent interest.