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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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