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Proceedings of the American Mathematical Society

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Isotopy equivalence classes of normal arcs in $ F\times I$


Author: C. D. Feustel
Journal: Proc. Amer. Math. Soc. 38 (1973), 393-399
MSC: Primary 55A25
DOI: https://doi.org/10.1090/S0002-9939-1973-0322847-6
MathSciNet review: 0322847
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Abstract: Let $ F$ be a compact $ 2$-manifold and $ I$ the closed unit interval. Let $ \alpha $ and $ \beta $ be arcs embedded in $ F \times I$ such that $ \alpha $ and $ \beta $ meet the boundary of $ F \times I$ in the boundary of $ \alpha $ and $ \beta $ respectively. Then we give necessary and sufficient conditions for the existence of an ambient isotopy, constant on the boundary of $ F \times I$, moving $ \alpha $ to $ \beta $. We also obtain ambient isotopies of families of arcs properly embedded in $ F \times I$.


References [Enhancements On Off] (What's this?)

  • [1] E. M. Brown, Unknotting in $ {M^2} \times I$, Trans. Amer. Math. Soc. 123 (1966), 480-505. MR 33 #6640. MR 0198482 (33:6640)
  • [2] E. M. Brown and R. H. Crowell, The augmentation subgroup of a link, J. Math. Mech. 15 (1966), 1065-1074. MR 33 #4920. MR 0196734 (33:4920)
  • [3] C. D. Feustel, Isotopic unknotting in $ F \times I$, Trans. Amer. Math. Soc. (to appear).
  • [4] J. Martin and D. Rolfsen, Homotopic arcs are isotopic, Proc. Amer. Math. Soc. 19 (1968), 1290-1292. MR 38 #719. MR 0232394 (38:719)
  • [5] A. Shapiro and J. H. C. Whitehead, A proof and extension of Dehn's lemma, Bull. Amer. Math. Soc. 64 (1958), 174-178. MR 21 #2242. MR 0103474 (21:2242)
  • [6] F. Waldhausen, On irreducible $ 3$-manifolds which are sufficiently large, Ann. of Math. (2) 87 (1968), 56-88. MR 36 #7146. MR 0224099 (36:7146)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0322847-6
Article copyright: © Copyright 1973 American Mathematical Society

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