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manuscripta mathematica

, Volume 107, Issue 4, pp 451–461 | Cite as

On the Grigorchuk–Kurchanov conjecture

  • Tullio G. Ceccherini-Silberstein
  • 38 Downloads

Abstract.

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

This leads to further investigations for splitting homomorphisms for the pairs (F 2 g , F g) and (G g, F g) where G g denotes the fundamental group of a closed orientable surface of genus g and a reformulation of the Poincaré and Grigorchuk–Kurchanov conjectures is derived.

Keywords

Free Group Fundamental Group Orientable Surface Normal Closure Closed Orientable Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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 C.so Garibaldi 107, 82100 Benevento, Italy. e-mail: tceccher@mat.uniroma1.itIT

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