On the Grigorchuk-Kurchanov conjecture

T. Ceccherini-Silberstein

Let F_m denote the free group of rank m.
The Grigorchuk-Kurchanov (briefly G-K) conjecture states that there exists a unique (up to a suitable
equivalence) epimorphism F_2m --> F_m x F_m .
We first observe that G-K holds for m=l, a characterization of generating automorphisms for F2 is
derived. Further investigations are presented for pairs (F_2m, F_m) and (G_g, F_g ) where G_g denotes the
fundamental group of a closed orientable surface of genus g.