Proper knots in open $3$-manifolds have locally unknotted representatives
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- by Ollie Nanyes
- Proc. Amer. Math. Soc. 113 (1991), 563-571
- DOI: https://doi.org/10.1090/S0002-9939-1991-1065089-2
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Abstract:
Churchard and Spring [1] conjectured that all proper knots in open $3$-manifolds are equivalent to (properly isotopic to) a locally unknotted proper knot. This paper proves the conjecture.References
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- Ralph H. Fox, A remarkable simple closed curve, Ann. of Math. (2) 50 (1949), 264–265. MR 30745, DOI 10.2307/1969450
- 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
- Dale Rolfsen, Knots and links, Mathematics Lecture Series, No. 7, Publish or Perish, Inc., Berkeley, Calif., 1976. MR 0515288
Bibliographic Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 563-571
- MSC: Primary 57M30; Secondary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-1991-1065089-2
- MathSciNet review: 1065089