Notions of spanning surface equivalence
Author:
Julian R. Eisner
Journal:
Proc. Amer. Math. Soc. 56 (1976), 345-348
MSC:
Primary 55A25; Secondary 57C25
DOI:
https://doi.org/10.1090/S0002-9939-1976-0402716-6
MathSciNet review:
0402716
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We show that two natural notions of spanning surface equivalence differ for minimal spanning surfaces of knots in .
- [1] W. R. Alford, Complements of minimal spanning surfaces of knots are not unique, Ann. of Math. (2) 91 (1970), 419–424 (French). MR 0253312, https://doi.org/10.2307/1970584
- [2] W. R. Alford and C. B. Schaufele, Complements of minimal spanning surfaces of knots are not unique. II., Topology of Manifolds (Proc. Inst., Univ. of Georgia, Athens, Ga., 1969), Markham, Chicago, Ill., 1970, pp. pp 87–96. MR 0288751
- [3] R. J. Daigle, Complements of minimal surfaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 22 (1974), 1021–1025 (English, with Russian summary). MR 0375283
- [4] R. J. Daigle, More on complements of minimal spanning surfaces, Rocky Mountain J. Math. 3 (1973), 473–482. MR 0367968, https://doi.org/10.1216/RMJ-1973-3-3-473
- [5] R. H. Fox, A quick trip through knot theory, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 120–167. MR 0140099
- [6] Herbert C. Lyon, Simple knots without unique minimal surfaces, Proc. Amer. Math. Soc. 43 (1974), 449–454. MR 0377850, https://doi.org/10.1090/S0002-9939-1974-0377850-8
- [7] L. P. Neuwirth, Knot groups, Annals of Mathematics Studies, No. 56, Princeton University Press, Princeton, N.J., 1965. MR 0176462
- [8] H. Seifert, Über das Geschlecht von Knoten, Math. Ann. 110 (1935), no. 1, 571–592 (German). MR 1512955, https://doi.org/10.1007/BF01448044
- [9]
J. R. Stallings, On fibering certain
-manifolds, Topology of
-Manifolds and Related Topics (Proc. Univ. of Georgia Inst., 1961, Prentice-Hall, Englewood Cliffs, N. J., 1962, pp. 95-100. MR 28 #1600.
- [10] H. F. Trotter, Some knots spanned by more than one knotted surface of mininal genus, Knots, groups, and 3-manifolds (papers dedicated to the memory of R. H. Fox), Princeton Univ. Press, Princeton, N.J., 1975, pp. 51–62. Ann. of Math. Studies, No. 84. MR 0377851
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55A25, 57C25
Retrieve articles in all journals with MSC: 55A25, 57C25
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1976-0402716-6
Keywords:
Knot,
composite knot,
minimal spanning surface,
isotopic deformation
Article copyright:
© Copyright 1976
American Mathematical Society