65 research outputs found
Cohomological dimension of Markov compacta
We rephrase Gromov's definition of Markov compacta, introduce a subclass of
Markov compacta defined by one building block and study cohomological
dimensions of these compacta. We show that for a Markov compactum ,
\dim_{\Z_{(p)}}X=\dim_{\Q}X for all but finitely many primes where
is the localization of at . We construct Markov compacta of
arbitrarily large dimension having \dim_{\Q}X=1 as well as Markov compacta of
arbitrary large rational dimension with for a given
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