Markov's theorem in 3--manifolds

Sofia Lambropoulou; Colin P. Rourke

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Markov's theorem in 3--manifolds

Sofia Lambropoulou·Colin P. Rourke

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Abstract

In this paper we first give a one-move version of Markov's braid theorem for knot isotopy in $S^3$ that sharpens the classical theorem. Then a relative version of Markov's theorem concerning a fixed braided portion in the knot. We also prove an analogue of Markov's theorem for knot isotopy in knot complements. Finally we extend this last result to prove a Markov theorem for links in an arbitrary orientable 3--manifold.

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BibTeX RIS

Sofia Lambropoulou, Colin P. Rourke. 2004-05-26. Markov's theorem in 3--manifolds. https://arxiv.org/abs/math/0405498

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