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This article is cited in 13 scientific papers (total in 13 papers)
Markov's theorem and algorithmically non-recognizable combinatorial manifolds
M. A. Shtan'ko
Abstract:
We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial $n$-dimensional manifold for every $n\geqslant 4$. We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all $n\geqslant 4$. We use Borisov's group [8] with
insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem. (The author is indebted to
S. I. Adian for this idea.)
Received: 30.01.2003
Citation:
M. A. Shtan'ko, “Markov's theorem and algorithmically non-recognizable combinatorial manifolds”, Izv. RAN. Ser. Mat., 68:1 (2004), 207–224; Izv. Math., 68:1 (2004), 205–221
Linking options:
https://www.mathnet.ru/eng/im471https://doi.org/10.1070/IM2004v068n01ABEH000471 https://www.mathnet.ru/eng/im/v68/i1/p207
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Abstract page: | 1123 | Russian version PDF: | 474 | English version PDF: | 35 | References: | 56 | First page: | 2 |
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