Markov's theorem in 3--manifolds

Details Markov's theorem in 3--manifolds Markov's theorem in 3--manifolds

2004-05-26

arxiv.org/abs/math/0405498v1

Topology and its Applications, Vol. 78, pp. 95--122 (1997)

Mathematics

Geometric Topology

29 pages, 41 figures, LaTex document

Scientific paper

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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