Counting coarse subsets of a countable group

Authors

DOI:

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

Keywords:

ballean, coarse structure, asymorphism, coarse equivalence

Abstract

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

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Author Biographies

Igor V. Protasov, Kyiv University

Department of Computer Science and Cybernetics

Ksenia Protasova, Kyiv University

Department of Computer Science and Cybernetics

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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Published

2018-04-02

How to Cite

[1]
I. V. Protasov and K. Protasova, “Counting coarse subsets of a countable group”, Appl. Gen. Topol., vol. 19, no. 1, pp. 85–90, Apr. 2018.

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