Isotopy equivalence classes of normal arcs in 𝐹×𝐼

Feustel, C. D.

doi:10.1090/S0002-9939-1973-0322847-6

Isotopy equivalence classes of normal arcs in $F\times I$
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Proc. Amer. Math. Soc. 38 (1973), 393-399 Request permission

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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