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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Morphismes injectifs entre groupes d'Artin–Tits

Eddy Godelle

Algebraic & Geometric Topology 2 (2002) 519–536

arXiv: math.GR/0207120

Abstract

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
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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