Algebraic and Geometric Topology 2 (2002), paper no. 25, pages 519-536.

Morphismes injectifs entre groupes d'Artin-Tits

Eddy Godelle

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].

Resume. On construit une classe de morphismes entre groupes d'Artin-Tits qui generalise celle construite par J. Crisp dans [Injective maps between Artin groups, Proceedings of the Special Year in Geometric Group Theory, Berlin, (1999), 119 -- 138]. On montre que leurs restrictions aux monoides respectent les formes normales, et que pour les groupes d'Artin-Tits de type FC ces morphismes sont injectifs. La demonstration du second resultat utilise le complexe de Deligne et les chemins cubiques normaux construits dans [G. Niblo et L. Reeves, The geometry of cube complexes and the complexity of their fundamental groups, Topology 37 (1998) 621-633] et [J.A. Altobelli et 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

AMS subject classification. Primary: 20F36. Secondary: 20F32,57M07.

DOI: 10.2140/agt.2002.2.519

E-print: arXiv:math.GR/0207120

Submitted: 11 October 2001. Accepted: 20 June 2002. Published: 28 June 2002.

Notes on file formats

Eddy Godelle
LAMFA CNRS 2270, Universite de Picardie-Jules Verne
Faculte de Mathematiques et d'Informatique
33 rue Saint-Leu, 80000 Amiens, France
Email: eddy.godelle@u-picardie.fr
URL: http://www.mathinfo.u-picardie.fr/godelle
AGT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to http://msp.warwick.ac.uk/.