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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Last modified: February 26, 2006