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- W4302777452 abstract "We prove two theorems about homotopies of curves on 2-dimensional Riemannian manifolds. We show that, for any epsilon > 0, if two simple closed curves are homotopic through curves of bounded length L, then they are also isotopic through curves of length bounded by L + epsilon. If the manifold is orientable, then for any epsilon > 0 we show that, if we can contract a curve gamma traversed twice through curves of length bounded by L, then we can also contract gamma through curves bounded in length by L + epsilon. Our method involves cutting curves at their self-intersection points and reconnecting them in a prescribed way. We consider the space of all curves obtained in this way from the original homotopy, and use a novel approach to show that this space contains a path which yields the desired homotopy." @default.
- W4302777452 created "2022-10-07" @default.
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- W4302777452 date "2013-11-04" @default.
- W4302777452 modified "2023-09-28" @default.
- W4302777452 title "Converting homotopies to isotopies and dividing homotopies in half in an effective way" @default.
- W4302777452 doi "https://doi.org/10.48550/arxiv.1311.0779" @default.
- W4302777452 hasPublicationYear "2013" @default.
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