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Reconstruction of braids. (English. Russian original) Zbl 0537.20017
Sib. Math. J. 24, 462-468 (1984); translation from Sib. Mat. Zh. 24, No. 3(139), 176-183 (1983).
A fragment of a braid is obtained by removing one of its strings. It is always possible to recover a braid from the collection of all of its fragments. There exists an algorithm which decides whether a sequence of braids is the collection of all fragments of some braid. Further two braids have the same collection of fragments if and only if they differ by a smooth braid.
Reviewer: S.Moran
MSC:
20F36 Braid groups; Artin groups
20F05 Generators, relations, and presentations of groups
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
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References:
[1] The Kourov Problem Book [in Russian], Inst. Mat., Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1978).
[2] A. A. Markov, Foundations of the Algebraic Theory of Braids [in Russian], Tr. Mat. Inst. Steklova Akad. Nauk SSSR,16 (1945).
[3] W. Burau, ?Über Zopfinvarianten,? Abh. Math. Sem. Hamburg Univ.,9, 117-124 (1932). · JFM 58.0614.03
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