Floyd, William J. Group completions and limit sets of Kleinian groups. (English) Zbl 0428.20022 Invent. Math. 57, 205-218 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 8 ReviewsCited in 81 Documents MSC: 20F65 Geometric group theory 30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization) 20H10 Fuchsian groups and their generalizations (group-theoretic aspects) 57S30 Discontinuous groups of transformations Keywords:finitely generated group; Cayley graph; compact metric space; geometrically finite Kleinian group; parabolic fixed points; limit points of the Kleinian group; fundamental polyhedron; fundamental group of closed hyperbolic manifold; polycyclic group with one end PDFBibTeX XMLCite \textit{W. J. Floyd}, Invent. Math. 57, 205--218 (1980; Zbl 0428.20022) Full Text: DOI EuDML References: [1] Abikoff, W.: On boundaries of Teichmüller spaces and on Kleinian groups, III. Acta. Math.134, 211-237 (1975) · Zbl 0322.30017 [2] Bass, H.: The degree of polynomial growth of finitely generated nilpotent groups. Proc. London Math. Soc.25, 603-614 (1972) · Zbl 0259.20045 [3] Beardon, A.F., Maskit, B.: Limit points of Kleinian groups and finite sided fundamental polyhedra. Acta Math.132, 1-12 (1974) · Zbl 0277.30017 [4] Freudenthal, H.: Neuaufbau der Endentheorie. Ann. of Math.43, 261-279 (1942) · Zbl 0060.40006 [5] Harvey, W.J. (Ed.): Discrete Groups and Automorphic Functions. New York: Academic Press 1978 · Zbl 0396.03045 [6] Hopf, H.: Enden offener Räume und unendliche diskontinuierliche Gruppen. Comment. Math. Helv.16, 81-100 (1944) · Zbl 0060.40008 [7] Magnus, W., Karass, A., Solitar, D.: Combinatorial Group Theory. New York: Interscience 1956 [8] Malcev, A.I.: On certain classes of infinite solvable groups. A.M.S. Translations2, 1-21 (1956) · Zbl 0070.25404 [9] Marden, A.: The geometry of finitely generated kleinian groups. Ann. of Math.99, 383-462 (1974) · Zbl 0282.30014 [10] Marden, A.: Isomorphisms between fuchsian groups, In: Advances in Complex Function Theory (W. Kirwan, L. Zalcman, Eds.). Lecture Notes in Math. 505, Berlin-Heidelberg-New York: Springer-Verlag 1976 · Zbl 0335.20024 [11] Marden, A., Maskit, B.: On the isomorphism theorem for Kleinian groups. Inventiones Math.51, 9-14 (1979) · Zbl 0399.30037 [12] Margulis, G.A.: Isometry of closed manifolds of constant negative curvature with the same fundamental group. Soviet Math. Dokl.11, 722-723 (1970) · Zbl 0213.48202 [13] Milnor, J.: A note on curvature and fundamental group. J. Diff. Geometry2, 1-7 (1968) · Zbl 0162.25401 [14] Milnor, J.: Growth of finitely generated solvable groups. J. Diff. Geometry2, 447-449 (1968) · Zbl 0176.29803 [15] Milnor, J.: Problem. Amer. Math. Monthly75, 685-686 (1968) [16] Milnor, J.: On fundamental groups of complete affinely flat manifolds. Advances in Math.25, 178-187 (1977) · Zbl 0364.55001 [17] Mostow, G.D.: Strong Rigidity of Locally Symmetric Spaces. Princeton: Princeton University Press 1973 · Zbl 0265.53039 [18] Nielsen, J.: Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen. Acta Math.50, 189-358 (1927) · JFM 53.0545.12 [19] Nielsen, J.: Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen, II. Acta Math.53, 1-76 (1929) · JFM 55.0971.01 [20] Nielsen, J.: Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen, III. Acta Math.58, 87-167 (1932) · JFM 58.0613.01 [21] Nielsen, J.: Abbildungsklassen endlicher Ordnung. Acta Math.75, 23-115 (1943) · Zbl 0027.26601 [22] Plante, J.F., Thurston, W.P.: Polynomial growth in holonomy groups of foliations. Comment. Math. Helv.51, 567-584 (1976) · Zbl 0348.57009 [23] Thurston, W.P.: The Geometry and Topology of 3-manifolds. In press (1980) [24] Tits, J.: Free subgroups in linear groups.J. Algebra20, 250-270 (1972) · Zbl 0236.20032 [25] Warfield, R.B., Jr.: Nilpotent Groups. Berlin: Springer-Verlag 1976 · Zbl 0347.20018 [26] Wolf, J.A.: Growth of finitely generated solvable groups and curvature of Riemannian manifolds. J. Diff. Geometry2, 421-446 (1968) · Zbl 0207.51803 [27] Zieschang, H.: Über Automorphismen ebener diskontinuierlicher Gruppen. Math. Ann.166, 148-167 (1966) · Zbl 0151.33102 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.