Semistability of amalgamated products, HNN-extensions, and all one-relator groups

Mihalik, Michael L.; Tschantz, Steven T.

doi:10.1090/S0273-0979-1992-00257-4

Semistability of amalgamated products, HNN-extensions, and all one-relator groups
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Bull. Amer. Math. Soc. 26 (1992), 131-135 Request permission

References

Mladen Bestvina and Geoffrey Mess, The boundary of negatively curved groups, J. Amer. Math. Soc. 4 (1991), no. 3, 469–481. MR 1096169, DOI 10.1090/S0894-0347-1991-1096169-1
Robert Bieri, Homological dimension of discrete groups, Queen Mary College Mathematics Notes, Queen Mary College, Mathematics Department, London, 1976. MR 0466344
Warren Dicks and M. J. Dunwoody, Groups acting on graphs, Cambridge Studies in Advanced Mathematics, vol. 17, Cambridge University Press, Cambridge, 1989. MR 1001965
M. J. Dunwoody, The accessibility of finitely presented groups, Invent. Math. 81 (1985), no. 3, 449–457. MR 807066, DOI 10.1007/BF01388581
Hans Freudenthal, Über die Enden topologischer Räume und Gruppen, Math. Z. 33 (1931), no. 1, 692–713 (German). MR 1545233, DOI 10.1007/BF01174375
Ross Geoghegan, The shape of a group—connections between shape theory and the homology of groups, Geometric and algebraic topology, Banach Center Publ., vol. 18, PWN, Warsaw, 1986, pp. 271–280. MR 925870
Ross Geoghegan and Michael L. Mihalik, Free abelian cohomology of groups and ends of universal covers, J. Pure Appl. Algebra 36 (1985), no. 2, 123–137. MR 787167, DOI 10.1016/0022-4049(85)90065-9
M. Gromov, Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 75–263. MR 919829, DOI 10.1007/978-1-4613-9586-7_{3}
Heinz Hopf, Enden offener Räume und unendliche diskontinuierliche Gruppen, Comment. Math. Helv. 16 (1944), 81–100 (German). MR 10267, DOI 10.1007/BF02568567
Brad Jackson, End invariants of group extensions, Topology 21 (1982), no. 1, 71–81. MR 630881, DOI 10.1016/0040-9383(82)90042-8
Roger C. Lyndon and Paul E. Schupp, Combinatorial group theory, Classics in Mathematics, Springer-Verlag, Berlin, 2001. Reprint of the 1977 edition. MR 1812024, DOI 10.1007/978-3-642-61896-3
Michael L. Mihalik, Semistability at the end of a group extension, Trans. Amer. Math. Soc. 277 (1983), no. 1, 307–321. MR 690054, DOI 10.1090/S0002-9947-1983-0690054-4
Michael L. Mihalik, Ends of groups with the integers as quotient, J. Pure Appl. Algebra 35 (1985), no. 3, 305–320. MR 777262, DOI 10.1016/0022-4049(85)90048-9
Michael L. Mihalik, Ends of double extension groups, Topology 25 (1986), no. 1, 45–53. MR 836723, DOI 10.1016/0040-9383(86)90004-2
Michael Mihalik, Semistability at $\infty$ of finitely generated groups, and solvable groups, Topology Appl. 24 (1986), no. 1-3, 259–269. Special volume in honor of R. H. Bing (1914–1986). MR 872498, DOI 10.1016/0166-8641(86)90069-6
Michael L. Mihalik, Semistability at $\infty$, $\infty$-ended groups and group cohomology, Trans. Amer. Math. Soc. 303 (1987), no. 2, 479–485. MR 902779, DOI 10.1090/S0002-9947-1987-0902779-7
Michael L. Mihalik and Steven T. Tschantz, Semistability of amalgamated products and HNN-extensions, Mem. Amer. Math. Soc. 98 (1992), no. 471, vi+86. MR 1110521, DOI 10.1090/memo/0471

All one relator groups are semistable at infinity

Peter Scott and Terry Wall, Topological methods in group theory, Homological group theory (Proc. Sympos., Durham, 1977) London Math. Soc. Lecture Note Ser., vol. 36, Cambridge Univ. Press, Cambridge-New York, 1979, pp. 137–203. MR 564422
Jean-Pierre Serre, Trees, Springer-Verlag, Berlin-New York, 1980. Translated from the French by John Stillwell. MR 607504, DOI 10.1007/978-3-642-61856-7
John Stallings, Group theory and three-dimensional manifolds, Yale Mathematical Monographs, vol. 4, Yale University Press, New Haven, Conn.-London, 1971. A James K. Whittemore Lecture in Mathematics given at Yale University, 1969. MR 0415622