Montesinos Amilibia, José María and González Acuña, Francisco Javier
(1978)
*Ends of knot groups.*
Annals of Mathematics, 108
(1).
pp. 91-96.
ISSN 0003-486X

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Official URL: http://www.jstor.org/stable/1970930

## Abstract

In 1962, R. H. Fox asked [Topology of 3-manifolds and related topics (Proc. Univ. Georgia Inst., 1961), pp. 168–176, especially pp. 175–176, Prentice-Hall, Englewood Cliffs, N.J., 1962)] whether a 2-knot group could have infinitely many ends. The authors answer this question in the affirmative by exhibiting 2-knots whose groups have infinitely many ends.

Item Type: | Article |
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Uncontrolled Keywords: | higher dimensional knot groups with infinitely many ends |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 17263 |

References: | J. J. ANDREWS and M. L. CURTIS, Free groups and handlebodies, Proc. A.M.S. 16 (1965), 192-195. E. ARTIN, Zur Isotopie zweidimensionalen Flichen im R4, Abh. Math. Sem. Univ. Ham- burg 4 (1926), 174-177. D. B. A. EPSTEIN, Ends, Topology of 3-Manifolds and Related Topics, M. K. Fort editor, Prentice Hall (1962). W. FEIT and J. G. THOMPSON, Solvability of groups of odd order, Pacific J. Math. 13 (1963), 775-1029. R. H. Fox, Some problems in knot theory, Topology of 3-Manifolds and Related Topics, M. K. Fort editor, Prentice Hall (1962). M. GERSTENHABER and 0. S. ROTHAUS, The solution of sets of equations in groups, Proc. N.A.S.U. 48 (1962), 1531-1533. B. HUPPERT, Endliche gruppen I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin (1967). M. KERVAIRE, Les noeuds de dimensions superieures, Bull. Soc. Math. France 93 (1965), 225-271. J. M. MONTESINOS, A note on Andrews-Curtis' conjecture (in preparation). CH. D. PAPAKYRIAKOPOULOS, On the ends of the fundamental groups of 3-manifolds, Comment. Math. Helv. 32 (1957), 85-92. J. STALLINGS, A finitely presented group whose 3-dimensional integral homology is not finitely generated, Amer. J. Math. 85 (1963), 541-543. J. STALLINGS, Group Theory and Three-Dimensional Manifolds, New Haven and London, Yale University Press (1971). D. W. SUMNERS, Homotopy torsion in codimension two knots, Proc. Amer. Math. Soc. 24 (1970), 229-240. J. H. C. WHITEHEAD, On the asphericity of regions in the 3-sphere, Fund. Math. 32 (1939), 149-166. E. C. ZEEMAN, Twisting spun knots, Trans. Amer. Math. Soc. 115 (1965), 471-495. |

Deposited On: | 29 Nov 2012 09:51 |

Last Modified: | 29 Nov 2012 09:51 |

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