|
Semistability of amalgamated products, HNN-extensions, and all one-relator groups
Author(s):
Michael
L.
Mihalik;
Steven
T.
Tschantz
Journal:
Bull. Amer. Math. Soc.
26
(1992),
131-136.
MSC (1991):
Primary 20F32;
Secondary 20E06, 57M20
MathSciNet review:
1107833
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- [1]
- M. Bestvina and G. Mess, The boundary of negatively curved groups, preprint, 1990. MR 1096169
- [2]
- R. Bieri, Homological dimension of discrete groups, Queen Mary College Math. Notes, London, 1976. MR 466344
- [3]
- W. Dicks and M. J. Dunwoody, Groups acting on graphs, Cambridge Univ. Press, Cambridge and New York, 1989. MR 1001965
- [4]
- M. J. Dunwoody, The accessibility of finitely presented groups, Invent. Math. \textbf{81} (1985), 449--457. MR 807066
- [5]
- H. Freudenthal, \"Uber die Enden topologischer R\"aume und Gruppen, Math. Z. \textbf{33 {\rm (1931)}}, 692--713. MR 1545233
- [6]
- R. Geoghegan, \emph{The shape of a group}, Banach Center Publ., vol. 18, PWN, Warsaw, 1986 pp.~271--280. MR 925870
- [7]
- R. Geoghegan and M. Mihalik, Free abelian cohomology of groups and ends of universal covers, J. Pure Appl. Algebra \textbf{36} (1985), 123--137. MR 787167
- [8]
- M. Gromov, \emph{Hyperbolic Groups}, Math. Sci. Res. Inst. Publ. series, vol. 8, Springer-Verlag, Berlin and New York pp.~75--263. MR 919829
- [9]
- H. Hopf, Enden offener Ra\"ume und unendliche diskontinuierliche Gruppen, Comment. Math. Helv \textbf{16} (1943), 81--100. MR 10267
- [10]
- B. Jackson, End invariants of groups extensions, Topology \textbf{21} (1982), 71--81. MR 630881
- [11]
- R. C. Lyndon and P. E. Schupp, Combinatorial group theory, Springer-Verlag, Berlin, Heidelberg and New York, 1970. MR 1812024
- [12]
- M. Mihalik, Semistability at the end of a group extension, Trans. Amer. Math. Soc. \textbf{277} (1983), 307--321. MR 690054
- [13]
- M. Mihalik, Ends of groups with the integers as quotients, J. Pure Appl. Algebra \textbf{35} (1985), 305--320. MR 777262
- [14]
- M. Mihalik, Ends of double extension groups, Topology \textbf{25} (1986), 45--53. MR 836723
- [15]
- M. Mihalik, Semistability at $\infty $ of finitely generated groups and solvable groups, Topology Appl. \textbf{24} (1986), 259--269. MR 872498
- [16]
- M. Mihalik, Semistability at $\infty ,\infty $-ended groups and group cohomology, Trans. Amer. Math. Soc. \textbf{303} (1987), 479--485. MR 902779
- [17]
- M. Mihalik and S. Tschantz, Semistability of amalgamated products and HNN-extensions, Mem. Amer. Math. Soc. (to appear). MR 1110521
- [18]
- M. Mihalik and S. Tschantz, All one relator groups are semistable at infinity, preprint, 1991. MR 1191381
- [19]
- G. P. Scott and T. Wall, \emph{Topological methods in group theory}, Cambridge Univ. Press, 1979 pp.~137--203. MR 564422
- [20]
- J.-P. Serre, Trees, Springer-Verlag, Berlin and New York, 1980. MR 607504
- [21]
- J. Stallings, Group theory and three dimensional manifolds, Yale Math. Mono., vol. 4, Yale Univ. Press, New Haven, CT, 1972. MR 415622
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(1991):
20F32, 20E06, 57M20
Retrieve articles in all Journals with MSC
(1991):
20F32, 20E06, 57M20
Additional Information:
DOI:
10.1090/S0273-0979-1992-00257-4
PII:
S 0273-0979(1992)00257-4
|