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Proceedings of the American Mathematical Society

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

 

 

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$.


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