Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Incoherent negatively curved groups


Author: Daniel T. Wise
Journal: Proc. Amer. Math. Soc. 126 (1998), 957-964
MSC (1991): Primary 20F32, 20F05
MathSciNet review: 1423338
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In part 1, a construction of Rips is modified so that it produces a CAT$(-1)$ group instead of a small-cancellation group. Thus, many of the applications of Rips' construction to small-cancellation groups may be applied to CAT$(-1)$ groups as well. Part 2 offers a simple way of producing incoherent groups.


References [Enhancements On Off] (What's this?)

  • [1] Gilbert Baumslag, Some problems on one-relator groups, Proceedings of the Second International Conference on the Theory of Groups (Australian Nat. Univ., Canberra, 1973) Springer, Berlin, 1974, pp. 75–81. Lecture Notes in Math., Vol. 372. MR 0364463
  • [2] G. Baumslag, M. R. Bridson, C. F. Miller III, H. Short, Subgroups of Automatic Groups, pre-print.
  • [3] G. Baumslag, C. F. Miller III, and H. Short, Unsolvable problems about small cancellation and word hyperbolic groups, Bull. London Math. Soc. 26 (1994), no. 1, 97–101. MR 1246477, 10.1112/blms/26.1.97
  • [4] Gilbert Baumslag and James E. Roseblade, Subgroups of direct products of free groups, J. London Math. Soc. (2) 30 (1984), no. 1, 44–52. MR 760871, 10.1112/jlms/s2-30.1.44
  • [5] Robert Bieri, Homological dimension of discrete groups, Mathematics Department, Queen Mary College, London, 1976. Queen Mary College Mathematics Notes. MR 0466344
  • [6] M. R. Bridson and A. Haefliger, Metric spaces of nonpositive curvature, to appear.
  • [7] S. M. Gersten, Questions on Geometric Group Theory for the Max Dehn Seminar, available by ftp at: ftp.math.utah.edu /u/ma/gersten/MaxDehnSeminar (1995).
  • [8] M. Gromov, Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 75–263. MR 919829, 10.1007/978-1-4613-9586-7_3
  • [9] Roger C. Lyndon and Paul E. Schupp, Combinatorial group theory, Springer-Verlag, Berlin-New York, 1977. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 89. MR 0577064
  • [10] E. Rips, Subgroups of small cancellation groups, Bull. London Math. Soc. 14 (1982), no. 1, 45–47. MR 642423, 10.1112/blms/14.1.45
  • [11] G. P. Scott, Finitely generated 3-manifold groups are finitely presented, J. London Math. Soc. (2) 6 (1973), 437–440. MR 0380763
  • [12] John Cossey (ed.), Problem section, Proceedings of the Second International Conference on the Theory of Groups (Australian Nat. Univ., Canberra, 1973) Springer, Berlin, 1974, pp. 733–740. Lecture Notes in Math., Vol. 372. MR 0364402

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 20F32, 20F05

Retrieve articles in all journals with MSC (1991): 20F32, 20F05


Additional Information

Daniel T. Wise
Affiliation: Department of Mathematics, Fine Hall, Princeton University, Princeton, New Jersey 08544
Address at time of publication: Department of Mathematics, White Hall, Cornell University, Ithaca, New York 14853
Email: daniwise@math.cornell.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04146-X
Received by editor(s): March 17, 1996
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1998 American Mathematical Society