Two-dimensional artin groups with CAT(0) dimension three

Geometriae Dedicata

Volumn 94, Issue 1, 2002, Pages 185-214

  Brady, Noel ^a   Crisp, John ^b  

^a UNIVERSITY OF OKLAHOMA   (United States)

^b UNIVERSITÉ DE BOURGOGNE   (France)

Author keywords

Artin group; Dimension; Nonpositive curvature

Indexed keywords

EID: 0036413274     PISSN: 00465755     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020962804856     Document Type: Article

References (19)

1. Bestvina, M.: Non-positively curved aspects of Artin groups of finite type, Geom. Topology 3 (1999), 269-302.
2. Brady, N. and Crisp, J.: On dimensions of CAT(0) and CAT(-1) complexes with the same hyperbolic group action (in preparation).
3. Brady, N. and Crisp, J.: Notes on a torsion free hyperbolic group which is CAT(0) in dimension 2 but CAT(-1) only in dimension 3, Preprint, ENS Lyon, 2001.
4. Brady, T.: Artin groups of finite type with three generators, Michigan Math. J. 47 (2000), no. 2, 313-324.
5. Brady, T. and McCammond, J. P.: Three-generator Artin groups of large type are biautomatic. J. Pure Appl. Algebra 151 (2000), 1-9.
6. Bridson, M. R.: On the existence of flat planes in spaces of non-positive curvature, Proc. Amer. Math. Soc. 123 (1995), 223-235.
7. Bridson, M. R.: Length functions, curvature and the dimension of discrete groups, Math. Res. Lett. 8 (4) (2001), 557-567.
8. Bridson, M. R. and Haefliger, A.: Metric Spaces of Non-Positive Curvature, Springer-Verlag, Berlin, 1999.
9. Charney, R. and Davis, M.: Finite K(π, 1)'s for Artin groups, In: F. Quinn (ed.), Prospects in Topology, Proc. Conference in Honor of William Browder, Ann. of Math. Stud. 138, Princeton Univ. Press, 1995, pp. 110-124.
10. Gromov, M.: Spaces and Questions, Geom. Funct. Anal. (2000), Special Vol., I, 118-161.
11. Ghys, E. and De la Harpe, P. (eds): Sur les groupes hyperboliques d'apres Mikhael Gromov, Progr. Math. 83, Birkhauser, Boston, 1990.
12. Hanham, P.: The CAT(0) dimension of 3-generator Artin groups (in preparation).
13. Hurewicz, W. and Wallmann, H.: Dimension Theory, Princeton Univ. Press, 1941.
14. Kapovich, M.: An example of a two-dimensional hyperbolic group which can't act on two-dimensional negatively curved complexes, Preprint, Utah, 1994.
15. Kleiner, B.: The local structure of length spaces with curvature bounded above, Math. Z. 231 (1999), 409-456.
16. van der Lek, H.: The homotopy type of complex hyperplane complements, PhD thesis, University of Nijmegen, Nijmegen, 1983.
17. Morita, K.: On the dimension of product spaces, Amer. J. Math. 75 (1953), 205-223.
18. Nikolaev, I. G.: The tangent cone of an Alexandrov space of curvature ≤ K. Manuscripta Math. 86 (1995), 683-689.
19. Peifer, D.: Artin groups of extra large type are biautomatic, J. Pure Appl. Algebra 110 (1996), 15-56.