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1998 | 42 | 1 | 49-56
Tytuł artykułu

On manifold spines and cyclic presentations of groups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This is a survey of results and open problems on compact 3-manifolds which admit spines corresponding to cyclic presentations of groups. We also discuss questions concerning spines of knot manifolds and regular neighborhoods of homotopically PL embedded compacta in 3-manifolds.
Słowa kluczowe
Rocznik
Tom
42
Numer
1
Strony
49-56
Opis fizyczny
Daty
wydano
1998
Twórcy
  • Dipartimento di Matematica, Università di Modena, Via Campi 213/B, 41100 Modena, Italy
  • Dipartimento di Matematica, Università di Milano, Via C. Saldini 50, 20133 Milano, Italy
  • Institute of Mathematics, University of Ljubljana, P.O. Box 2964, Ljubljana 1001, Slovenia
Bibliografia
  • [1] B. G. Casler, An embedding theorem for connected 3-manifolds with boundary, Proc. Amer. Math. Soc. 16 (1965), 559-566.
  • [2] A. Cavicchioli, Imbeddings of polyhedra in 3-manifolds, Annali di Mat. Pura ed Appl. 162 (1992), 157-177.
  • [3] A. Cavicchioli, Neuwirth manifolds and colourings of graphs, Aequationes Math. 44 (1992), 168-187.
  • [4] A. Cavicchioli and F. Hegenbarth, Knot manifolds with isomorphic spines, Fund. Math. 145 (1994), 79-89.
  • [5] A. Cavicchioli, F. Hegenbarth and A. C. Kim, A geometric study of Sieradski groups, Algebra Colloq. 5 (1998), to appear.
  • [6] A. Cavicchioli, W. B. R. Lickorish and D. Repovš, On the equivalent spines problem, Boll. Un. Mat. Ital., to appear.
  • [7] A. Cavicchioli and D. Repovš, Peripheral acyclicity and homology manifolds, Annali di Mat. Pura ed Appl. 172 (1997), 5-24.
  • [8] A. Cavicchioli and F. Spaggiari, The classification of 3-manifolds with spines related to Fibonacci groups, in 'Algebraic Topology-Homotopy and Group Cohomology', Lect. Notes in Math., Springer Verlag 1509 (1992), 50-78.
  • [9] H. Helling, A. C. Kim and J. L. Mennicke, A geometric study of Fibonacci groups, Preprint Universitat Bielefeld 343 (1990).
  • [10] H. M. Hilden, M. T. Lozano and J. M. Montesinos, The arithmeticity of the figure eight knot orbifolds, in 'Topology '90', Walter de Gruyter Ed., Berlin - New York (1992), 169-183.
  • [11] C. Hog-Angeloni, W. Metzler and A. J. Sieradski, Two-dimensional homotopy and combinatorial group theory, London Math. Soc. Lect. Note Ser. 197, Cambridge Univ. Press, Cambridge, 1993.
  • [12] J. Howie, Cyclic presentations and (2,2k+1) torus knots, unpublished.
  • [13] A. C. Kim, On the Fibonacci group and related topics, Contemporary Math. 184 (1995), 231-235.
  • [14] D. L. Johnson and W. K. Odoni, Some results on symmetrically presented groups, Proceed. Edinburgh Math. Soc. 37 (1994), 227-237.
  • [15] A. Mednykh and A. Vesnin, Hyperbolic volumes of Fibonacci manifolds, Siberian Math. J. 36 (1995), 235-245.
  • [16] J. L. Mennicke, On Fibonacci groups and some other groups, Proceed. of Groups-Korea 1988, Pusan, August 1988, 117-123.
  • [17] J. Milnor, On the 3-dimensional Brieskorn manifolds M(p,q,r), in 'Knots, Groups and 3-Manifolds' (L. P. Neuwirth Ed.), Ann. of Math. Studies 84, Princeton Univ. Press, Princeton, N. J., 1975, 175-225.
  • [18] W. J. R. Mitchell, J. H. Przytycki and D. Repovš, On spines of knot spaces, Bull. Polish Acad. Sci. 37 (1989), 563-565.
  • [19] L. Neuwirth, An algorithm for the construction of 3-manifolds from 2-complexes, Proc. Camb. Phil. Soc. 64 (1968), 603-613.
  • [20] D. Repovš, Regular neighbourhoods of homotopically PL embedded compacta in 3-manifolds, Suppl. Rend. Circ. Mat. Palermo 18 (1988), 415-422.
  • [21] P. Scott, The Geometries of 3-manifolds, Bull. London Math. Soc. 15 (1983), 401-487.
  • [22] A. J. Sieradski, Combinatorial squashings, 3-manifolds, and the third homotopy of groups, Invent. Math. 84 (1986), 121-139.
  • [23] R. Thomas, On a question of Kim concerning certain group presentations, Bull. Korean Math. Soc. 28 (1991), 219-244.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv42i1p49bwm
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