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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 $$\mathbb{R}^4$$.
 57Q45 Knots and links in high dimensions (PL-topology) (MSC2010) 57M25 Knots and links in the $$3$$-sphere (MSC2010)
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