Pseudo-isotopies of arcs and knots
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- by Carl D. Sikkema PDF
- Proc. Amer. Math. Soc. 31 (1972), 615-616 Request permission
Abstract:
The purpose of this paper is to show that if an arc or simple closed curve contains a nontrivial Wilder arc, then it is not possible to transform a straight line segment onto the arc or a knot onto the simple closed curve. The proof uses the fact that every knot has a unique finite decomposition into prime knots.References
- Ralph H. Fox and Emil Artin, Some wild cells and spheres in three-dimensional space, Ann. of Math. (2) 49 (1948), 979–990. MR 27512, DOI 10.2307/1969408
- 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
- R. H. Fox and O. G. Harrold, The Wilder arcs, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 184–187. MR 0140096
- O. G. Harrold Jr., Combinatorial structures, local unknottedness, and local peripheral unknottedness, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 71–83. MR 0158372
- Ljudmila Keldyš, Topological imbeddings and pseudo-isotropy, Dokl. Akad. Nauk SSSR 169 (1966), 1262–1265 (Russian). MR 0203707
- Ljudmila Keldyš, Topological imbeddings into a manifold and pseudoisotopy, Mat. Sb. (N.S.) 71 (113) (1966), 433–453 (Russian). MR 0206968
- L. V. Keldyš, Topological imbedding in $E^{3}$ of simple arcs and closed contours, Dokl. Akad. Nauk SSSR 185 (1969), 513–516 (Russian). MR 0240796
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 615-616
- DOI: https://doi.org/10.1090/S0002-9939-1972-0286094-8
- MathSciNet review: 0286094