There exist arbitrarily many different disk knots with the same exterior
HTML articles powered by AMS MathViewer
- by L. R. Hitt and D. W. Sumners PDF
- Proc. Amer. Math. Soc. 86 (1982), 148-150 Request permission
Abstract:
We prove that, for $n \geqslant 5$, exteriors of disk knots of ${D^n}$ in ${D^{n + 2}}$ can be exteriors of arbitrarily many different disk knots.References
- Jean Dieudonné, La géométrie des groupes classiques, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963 (French). Seconde édition, revue et corrigée. MR 0158011
- C. McA. Gordon, Homology of groups of surfaces in the $4$-sphere, Math. Proc. Cambridge Philos. Soc. 89 (1981), no. 1, 113–117. MR 591977, DOI 10.1017/S0305004100057996 F. González-Acuña, personal correspondence.
- L. R. Hitt and D. W. Sumners, Many different disk knots with the same exterior, Comment. Math. Helv. 56 (1981), no. 1, 142–147. MR 615622, DOI 10.1007/BF02566205
- B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703
- Mitsuyoshi Kato, Higher dimensional $\textrm {PL}$ knots and knot manifolds, J. Math. Soc. Japan 21 (1969), 458–480. MR 248847, DOI 10.2969/jmsj/02130458
- Michel A. Kervaire, Smooth homology spheres and their fundamental groups, Trans. Amer. Math. Soc. 144 (1969), 67–72. MR 253347, DOI 10.1090/S0002-9947-1969-0253347-3
- Joseph J. Rotman, The theory of groups. An introduction, Allyn and Bacon, Inc., Boston, Mass., 1965. MR 0204499
- Robert Steinberg, Lectures on Chevalley groups, Yale University, New Haven, Conn., 1968. Notes prepared by John Faulkner and Robert Wilson. MR 0466335
- D. W. Sumners, Homotopy torsion in codimension two knots, Proc. Amer. Math. Soc. 24 (1970), 229–240. MR 253316, DOI 10.1090/S0002-9939-1970-0253316-7
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 148-150
- MSC: Primary 57Q45
- DOI: https://doi.org/10.1090/S0002-9939-1982-0663885-9
- MathSciNet review: 663885