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Morphismes injectifs entre groupes d'Artin-Tits | | Eddy Godelle
; | | Date: |
15 Jul 2002 | | Journal: | Algebr. Geom. Topol. 2 (2002) 519-536 | | Subject: | Group Theory; Geometric Topology MSC-class: 20F36, 20F32,57M07 | math.GR math.GT | | 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]. | | Source: | arXiv, math.GR/0207120 | | Services: | Forum | Review | PDF | Favorites | |
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