FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 5, PAGES 257-259

To the Markov theorem on algorithmic nonrecognizability of manifolds

M. A. Stan'ko

Abstract

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We prove that the number of summands in the connected union of product of spheres which is algorithmically nonrecognizable, as was shown earlier, can be reduced to 14. Also, we note that the manifold constructed by Markov himself in his original work on topological nonrecognizability coincides with such union (where the number of summands is equal to the quantity of relations in group representations of the corresponding Adian sequence).

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