Counting coarse subsets of a countable group

Igor V. Protasov

https://orcid.org/0000-0003-1518-6234

Ukraine

Kyiv University

Department of Computer Science and Cybernetics

Ksenia Protasova

https://orcid.org/0000-0002-7991-8273

Ukraine

Kyiv University

Department of Computer Science and Cybernetics

Submitted: 2017-05-31

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Accepted: 2017-09-10

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Published: 2018-04-02

DOI: https://doi.org/10.4995/agt.2018.7721
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Keywords:

ballean, coarse structure, asymorphism, coarse equivalence

Supporting agencies:

This research was not funded

Abstract:

For every countable group G, there are 2ω distinct classes of coarselyequivalent subsets of G.

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References:

T. Banakh, J. Higes and M. Zarichnyi, The coarse classification of countable abelian groups, Trans. Amer. Math. Soc. 362 (2010), 4755-4780. https://doi.org/10.1090/S0002-9947-10-05118-4

D. Dikranjan and N. Zava, Some categorical aspects of coarse spaces and ballean, Topology Appl. 225 (2017) 164-194. https://doi.org/10.1016/j.topol.2017.04.011

P. de la Harpe, Topics in geometric group theory, University Chicago Press, 2000.

I. V. Protasov, Morphisms of ball structures of groups and graphs, Ukr. Mat. Zh. 53 (2002), 847-855.

I. Protasov and T. Banakh, Ball structures and colorings of groups and graphs, Math. Stud. Monogr. Ser., Vol. 11, VNTL, Lviv, 2003.

I. Protasov and M. Zarichnyi, General asymptology, Math. Stud. Monogr. Ser., Vol. 12, VNTL, Lviv, 2007.

J. Roe, Lectures on coarse geometry, Amer. Math. Soc., Providence, R.I, 2003.

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