×

Semistability of amalgamated products, HNN-extensions, and all one- relator groups. (English) Zbl 0818.20044

Announcement of results. The details have appeared [in Mem. Am. Math. Soc. 98 (1992; Zbl 0792.20027)].

MSC:

20F65 Geometric group theory
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
57M05 Fundamental group, presentations, free differential calculus
20F05 Generators, relations, and presentations of groups
20J05 Homological methods in group theory
57M10 Covering spaces and low-dimensional topology

Citations:

Zbl 0792.20027
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Mladen Bestvina and Geoffrey Mess, The boundary of negatively curved groups, J. Amer. Math. Soc. 4 (1991), no. 3, 469 – 481. · Zbl 0767.20014
[2] Robert Bieri, Homological dimension of discrete groups, Mathematics Department, Queen Mary College, London, 1976. Queen Mary College Mathematics Notes. · Zbl 0357.20027
[3] Warren Dicks and M. J. Dunwoody, Groups acting on graphs, Cambridge Studies in Advanced Mathematics, vol. 17, Cambridge University Press, Cambridge, 1989. · Zbl 0665.20001
[4] M. J. Dunwoody, The accessibility of finitely presented groups, Invent. Math. 81 (1985), no. 3, 449 – 457. · Zbl 0572.20025 · doi:10.1007/BF01388581
[5] Hans Freudenthal, Über die Enden topologischer Räume und Gruppen, Math. Z. 33 (1931), no. 1, 692 – 713 (German). · Zbl 0002.05603 · doi:10.1007/BF01174375
[6] 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. · Zbl 0641.55009
[7] 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. · Zbl 0577.20024 · doi:10.1016/0022-4049(85)90065-9
[8] M. Gromov, Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 75 – 263. · Zbl 0634.20015 · doi:10.1007/978-1-4613-9586-7_3
[9] Heinz Hopf, Enden offener Räume und unendliche diskontinuierliche Gruppen, Comment. Math. Helv. 16 (1944), 81 – 100 (German). · Zbl 0060.40008 · doi:10.1007/BF02568567
[10] Brad Jackson, End invariants of group extensions, Topology 21 (1982), no. 1, 71 – 81. · Zbl 0472.57001 · doi:10.1016/0040-9383(82)90042-8
[11] Roger C. Lyndon and Paul E. Schupp, Combinatorial group theory, Classics in Mathematics, Springer-Verlag, Berlin, 2001. Reprint of the 1977 edition. · Zbl 0368.20023
[12] Michael L. Mihalik, Semistability at the end of a group extension, Trans. Amer. Math. Soc. 277 (1983), no. 1, 307 – 321. · Zbl 0518.57002
[13] Michael L. Mihalik, Ends of groups with the integers as quotient, J. Pure Appl. Algebra 35 (1985), no. 3, 305 – 320. · Zbl 0589.20018 · doi:10.1016/0022-4049(85)90048-9
[14] Michael L. Mihalik, Ends of double extension groups, Topology 25 (1986), no. 1, 45 – 53. · Zbl 0589.57001 · doi:10.1016/0040-9383(86)90004-2
[15] 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). · Zbl 0612.57002 · doi:10.1016/0166-8641(86)90069-6
[16] Michael L. Mihalik, Semistability at \infty , \infty -ended groups and group cohomology, Trans. Amer. Math. Soc. 303 (1987), no. 2, 479 – 485. · Zbl 0641.57001
[17] Michael L. Mihalik and Steven T. Tschantz, Semistability of amalgamated products and HNN-extensions, Mem. Amer. Math. Soc. 98 (1992), no. 471, vi+86. , https://doi.org/10.1090/memo/0471 Michael L. Mihalik and Steven T. Tschantz, Semistability of amalgamated products, HNN-extensions, and all one-relator groups, Bull. Amer. Math. Soc. (N.S.) 26 (1992), no. 1, 131 – 135. · Zbl 0792.20027
[18] -, All one relator groups are semistable at infinity, preprint, 1991.
[19] 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. · Zbl 0423.20023
[20] Jean-Pierre Serre, Trees, Springer-Verlag, Berlin-New York, 1980. Translated from the French by John Stillwell. · Zbl 0548.20018
[21] John Stallings, Group theory and three-dimensional manifolds, Yale University Press, New Haven, Conn.-London, 1971. A James K. Whittemore Lecture in Mathematics given at Yale University, 1969; Yale Mathematical Monographs, 4. · Zbl 0241.57001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.