The tits conjecture for locally reducible artin groups

International Journal of Algebra and Computation

Volumn 10, Issue 6, 2000, Pages 783-797

  Charney, Ruth ^a  

^a OHIO STATE UNIVERSITY   (United States)

Author keywords

Artin groups; CAT(0) spaces

Indexed keywords

EID: 0034552875     PISSN: 02181967     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218196700000479     Document Type: Article

References (26)

1. J. Altobelli and R. Charney, A geometric rational form for Artin groups of FC type, Geometriae Dedicata 79 (2000), 277-289.
2. K. I. Appel and P. E. Schupp, Artin groups and infinite Coxeter groups, Invent. Math. 72 (1983), 201-220.
3. M. Bestvina and N. Brady, Morse theory and finiteness properties of groups, Invent. Math. 109 (1997), 445-470.
4. M. Bestvina, Non-positively curved aspects of Artin groups of finite type, Geometry and Topology 3 (1999), 269-302.
5. M. Bridson and A. Haefliger, Metric Spaces of Non-positive Curvature, Springer-Verlag, 1999.
6. T. Brady and J. McCammond, Three-generator Artin groups of large type are biautomatic, J. Pure Appl. Algebra 151 (2000), 1-9.
7. M. R. Bridson, Geodesics and curvature in metric simplicial complexes, Group Theory from a Geometrical Viewpoint, eds. E. Ghys, A. Haefliger and A. Verjovsky, World Scientific, Singapore, 1991, pp. 373-463.
8. K. Brown, Buildings, Springer-Verlag, New York, 1989.
9. E. Brieskorn and K. Saito, Artin-gruppen und Coxeter-gruppen, Invent. Math. 17 (1972), 245-271.
10. R. Charney, Artin groups of finite type are biautomatic, Math. Ann. 292 (1992), 671-683.
11. _, Geodesic automation and growth functions for Artin groups of finite type, Math. Ann. 301 (1995), 307-324.
12. _, Injectivity of the positive monoid for some infinite type Artin groups, Geometric Group Theory Down Under, eds. J. Cossey, C. Miller, W. Neumann and M. Shapiro, Walter de Gruyter, Berlin, 1999.
13. R. Charney and M. W. Davis, The K(π, 1)-problem for hyperplane complements associated to infinite reflection groups, J. Amer. Math. Soc. 8 (1995), 597-627.
14. _, Singular metrics of nonpositive curvature on branched covers of Riemannian manifolds, Amer. J. Math. 115 (1993), 929-1009.
15. D. Collins, Relations among the squares of the generators of the braid group, Invent. Math. 117 (1994), 525-529.
16. P. Deligne, Les immeubles des groups de tresses généralisés, Invent. Math. 17 (1972), 273-302.
17. C. Droms, J. Lewin and H. Servatius, Tree groups and the 4-string pure braid group, J. Pure Appl. Algebra 70 (1991), 251-261.
18. _, The Tits conjecture and the five string braid group, Topology and Combinatorial Group Theory, ed. P. Latiolois, LNM 1440, Springer, 1990, pp. 48-51.
19. M. Gromov, Hyperbolic groups, Essays in Group Theory, ed. S. M. Gersten, MSRI Publ. 8, Springer-Verlag, New York, 1987, pp. 75-264.
20. F. A. Garside, The braid groups and other groups, Quart. J. Math. Oxford 20 (1969), 235-254.
21. S. P. Humphries, On representations of the Artin groups and the Tits conjecture, J. Algebra 169 (1994), 847-862.
22. H. van der Lek, The homotopy type of complex hyperplane complements, Ph.D. Thesis, University of Nijmegen, 1983.
23. G. Moussong, Hyperbolic Coxeter groups, Ph.D. Thesis, The Ohio State University, 1988.
24. J. Tits, Normalisateurs de tores. I. Groups de Coxeter étendus, J. Algebra 4 (1966), 96-116.
25. D. Peifer, Artin groups of extra-large type are biautomatic, J. Pure Appl. Algebra 110 (1996), 15-56.
26. S. J. Pride, On Tits' conjecture and other questions concerning Artin and generalized Artin groups, Invent. Math. 86 (1986), 347-356.