“Markov's theorem

[Stephen P. King]

Hi Bruno and Russell,

    This is one of the reasons I am skeptical of Bruno's immaterialism:
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=im&paperid=471&option_lang=eng


Markov's theorem and algorithmically non-recognizable combinatorial 
manifolds

M. A. Shtan'ko 
<http://www.mathnet.ru/php/person.phtml?option_lang=eng&personid=8892>


*Abstract:* We prove the theorem of Markov on the existence of an 
algorithmically non-recognizable combinatorial
-dimensional manifold for every . 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 . 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.


--
Onward!

Stephen

"Nature, to be commanded, must be obeyed."
~ Francis Bacon

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