Bulletin of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-9485(e) ISSN 0273-0979(p)

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), 131-135.
MSC (2000): Primary 57M07; Secondary 20E06, 20F32
MathSciNet review: 1107833
Retrieve article in: PDF

References:

[1]: M. Bestvina and G. Mess, The boundary of negatively curved groups, preprint, 1990. MR 1096169 (93j:20076)
[2]: R. Bieri, Homological dimension of discrete groups, Queen Mary College Math. Notes, London, 1976. MR 0466344 (57:6224)
[3]: W. Dicks and M. J. Dunwoody, Groups acting on graphs, Cambridge Univ. Press, Cambridge and New York, 1989. MR 1001965 (91b:20001)
[4]: M. J. Dunwoody, The accessibility of finitely presented groups, Invent. Math. 81 (1985), 449-457. MR 807066 (87d:20037)
[5]: H. Freudenthal, Über die Enden toplogischer Räume und Gruppen, Math. Z. 33 (1931), 692-713. MR 1545233
[6]: R. Geoghegan, The shape of a group, Geometric and Algebraic Topology (H. Torunczyk, ed.), Banach Center Publ., vol. 18, PWN, Warsaw, 1986, pp. 271-280. MR 925870 (89a:20057)
[7]: R. Geoghegan and M. Mihalik, Free abelian cohomology of groups and ends of universal covers, J. Pure Appl. Algebra 36 (1985), 123-137. MR 787167 (86h:20074)
[8]: M. Gromov, Hyperbolic Groups, Essays in Group Theory (S. M. Gersten, ed.), Math. Sci. Res. Inst. Publ. series, vol. 8, Springer-Verlag, Berlin and New York, pp. 75-263. MR 919829 (89e:20070)
[9]: H. Hopf, Enden offener Räume und unendliche diskontinuierliche Gruppen, Comment. Math. Helv. 16 (1943), 81-100. MR 0010267 (5:272e)
[10]: B. Jackson, End invariants of groups extensions, Topology 21 (1982), 71-81. MR 630881 (83a:57002)
[11]: R. C. Lyndon and P. E. Schupp, Combinatorial group theory, Springer-Verlag, Berlin, Heidelberg and New York, 1970. MR 1812024 (2001i:20064)
[12]: M. Mihalik, Semistability at the end of a group extension, Trans. Amer. Math. Soc. 277 (1983), 307-321. MR 690054 (84d:57001)
[13]: -, Ends of groups with the integers as quotients, J. Pure Appl. Algebra 35 (1985), 305-320. MR 777262 (86f:20060)
[14]: -, Ends of double extension groups, Topology 25 (1986), 45-53. MR 836723 (88c:57006)
[15]: -, Semistability at $\infty$ of finitely generated groups and solvable groups, Topology Appl. 24 (1986), 259-269. MR 872498 (88c:57005)
[16]: -, Semistability at $\infty$ , $\infty$ -ended groups and group cohomology, Trans. Amer. Math. Soc. 303 (1987), 479-485. MR 902779 (89b:20063)
[17]: M. Mihalik and S. Tschantz, Semistability of amalgamated products and HNN-extensions, Mem. Amer. Math. Soc. (to appear). MR 1110521 (92k:57002a)
[18]: -, All one relator groups are semistable at infinity, preprint, 1991.
[19]: G. P. Scott and T. Wall, Topological methods in group theory, London Math. Soc. Lecture Note Ser., vol. 36, Cambridge Univ. Press, 1979, pp. 137-203. MR 564422 (81m:57002)
[20]: J.-P. Serre, Trees, Springer-Verlag, Berlin and New York, 1980. MR 607504 (82c:20083)
[21]: J. Stallings, Group theory and three dimensional manifolds, Yale Math. Mono., vol. 4, Yale Univ. Press, New Haven, CT, 1972. MR 0415622 (54:3705)

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|