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Alexander’s and Markov’s theorems in dimension four. (English) Zbl 0831.57013
Every link type in \(\mathbb{R}^3\) is represented by a closed braid, and two closed braids represent the same link type if and only if they are related by braid isotopies, stabilizations, and their inverse operations. These facts are well-known as Alexander’s theorem and Markov’s theorem, and play an important role in knot theory. In this paper an analogous result is given for surface-link types in \(\mathbb{R}^4\).
Reviewer: S.Kamada (Osaka)

MSC:
57Q45 Knots and links in high dimensions (PL-topology) (MSC2010)
57M25 Knots and links in the \(3\)-sphere (MSC2010)
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