manuscripta mathematica

, Volume 107, Issue 4, pp 451–461

On the Grigorchuk–Kurchanov conjecture

  • Tullio G. Ceccherini-Silberstein

DOI: 10.1007/s002290200246

Cite this article as:
Ceccherini-Silberstein, T. Manuscripta Math. (2002) 107: 451. doi:10.1007/s002290200246


 Let \(\) denote the free group of rank 2g. An automorphism φ? Aut(F2g) is generating if Naφ (Nb) = F2g, where Na is the normal closure of \(\) and Nb is defined analogously. We present a characterization of generating automorphisms in Aut(F2) and observe that there exists a unique (up to equivalence) epimorphism F2Z×Z: this is a particular case of the Grigorchuk–Kurchanov conjecture.

This leads to further investigations for splitting homomorphisms for the pairs (F2g, Fg) and (Gg, Fg) where Gg denotes the fundamental group of a closed orientable surface of genus g and a reformulation of the Poincaré and Grigorchuk–Kurchanov conjectures is derived.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Tullio G. Ceccherini-Silberstein
    • 1
  1. 1.Dipartimento di Ingegneria, Università degli Studi del Sannio, Palazzo dell'Aquila-Bosco-Lucarelli Garibaldi 107, 82100 Benevento, Italy. e-mail: tceccher@mat.uniroma1.itIT