Incoherent negatively curved groups

Author:
Daniel T. Wise

Journal:
Proc. Amer. Math. Soc. **126** (1998), 957-964

MSC (1991):
Primary 20F32, 20F05

DOI:
https://doi.org/10.1090/S0002-9939-98-04146-X

MathSciNet review:
1423338

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Abstract | References | Similar Articles | Additional Information

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

**[1]**G. Baumslag,*Some Problems in One-Relator Groups*, in: Proc. Conf. Canberra 1973, Lecture notes in Math Vol. 372 (1973), 75-81. MR**51:717****[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, H. Short,*Unsolvable problems about Small Cancellation and Word Hyperbolic Groups*, Bull. London Math. Soc.**26**(1994), 97-101. MR**94i:20053****[4]**G. Baumslag and J. E. Roseblade,*Subgroups of Direct Product of Two Free Groups*, J. London Math. Soc. (2)**30**(1984), 44-52. MR**86d:20028****[5]**R. Bieri,*Homological dimension of discrete groups; Queen Mary College Math. Notes*, Queen Mary College, London, 1976. MR**57:6224****[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*, in: Essays in Group Theory (S.M. Gersten ed.) (1987). MR**89e:20070****[9]**R. C. Lyndon, and P. E. Schupp,*Combinatorial Group Theory*, Springer-Verlag, 1977. MR**58:28182****[10]**E. Rips,*Subgroups of Small Cancellation Groups*, Bull. London Math. Soc. (1982), 45-47. MR**83c:20049****[11]**G. P. Scott,*Finitely generated 3-manifold groups are finitely presented*, J. London Math. Soc.**6**(1973), 437-440. MR**52:1660****[12]**J. P. Serre,*Problems*, in: Proc. Conf. Canberra 1973, Lecture notes in Math Vol. 372 (1974), 734-735. MR**51:656**

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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:
https://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