Geodesic
Morphismes injectifs entre groupes d’Artin–Tits
Godelle, Eddy1
1LAMFA CNRS 2270, Université de Picardie-Jules Verne, Faculté de Mathématiques et d’Informatique, 33 rue Saint-Leu, 80000 Amiens, France
Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 519-536
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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].

DOI : 10.2140/agt.2002.2.519
Keywords: Artin–Tits groups, injective morphisms, cubical CAT(0) complex

Godelle, Eddy  1

1 LAMFA CNRS 2270, Université de Picardie-Jules Verne, Faculté de Mathématiques et d’Informatique, 33 rue Saint-Leu, 80000 Amiens, France 
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Godelle, Eddy. Morphismes injectifs entre groupes d’Artin–Tits. Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 519-536. doi: 10.2140/agt.2002.2.519

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