Morphismes injectifs entre groupes d’Artin–Tits

We construct a family of morphisms between Artin–Tits groups which generalise the ones constructed by J. Crisp in [Injective maps between Artin groups, Proceedings of the Special Year in Geometric Group Theory, Berlin, (1999), 119–138]. We show that their restrictions to the positive Artin monoids respect normal forms, and that for Artin–Tits groups of type FC, these morphisms are injective. The proof of the second result uses the Deligne Complex, and the normal cube paths constructed in [G. Niblo and L. Reeves, The geometry of cube complexes and the complexity of their fundamental groups, Topology 37 (1998) 621–633] and [J.A. Altobelli and R. Charney, A geometric Rational Form for Artin Groups of FC type, Geom. Dedicata, 79 (2000) 277–289].

Keywords

Artin–Tits groups, injective morphisms, cubical CAT(0) complex

Mathematical Subject Classification 2000

Primary: 20F36

Secondary: 20F32, 57M07

References

Forward citations

Publication

Received: 11 October 2001

Accepted: 20 June 2002

Published: 28 June 2002

Authors

Eddy Godelle
LAMFA CNRS 2270 Université de Picardie-Jules Verne Faculté de Mathématiques et d’Informatique 33 rue Saint-Leu 80000 Amiens France
http://www.mathinfo.u-picardie.fr/godelle

Volume 2, issue 1 (2002)

Eddy Godelle