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Keywords:
Higson corona; coarse geometry
Summary:
This paper discusses properties of the Higson corona by means of a quotient on coarse ultrafilters on a proper metric space. We use this description to show that the corona functor is faithful and reflects isomorphisms.
References:
[1] Baladze V., Dumbadze F.: On (co)homological properties of Stone–Čech compactifications of completely regular spaces. available at arXiv:1806.01566 [math.AT] (2018), 12 pages. MR 4036389
[2] Ball B. J., Yokura S.: Compactifications determined by subsets of $C^\ast (X)$. II. Topology Appl. 15 (1983), no. 1, 1–6. DOI 10.1016/0166-8641(83)90041-X | MR 0676960
[3] Banakh T., Chervak O., Zdomskyy L.: On character of points in the Higson corona of a metric space. Comment. Math. Univ. Carolin. 54 (2013), no. 2, 159–178. MR 3067701
[4] Cornulier Y., de la Harpe P.: Metric Geometry of Locally Compact Groups. EMS Tracts in Mathematics, 25, European Mathematical Society (EMS), Zürich, 2016. MR 3561300
[5] Dranishnikov A. N., Keesling J., Uspenskij V. V.: On the Higson corona of uniformly contractible spaces. Topology 37 (1998), no. 4, 791–803. DOI 10.1016/S0040-9383(97)00048-7 | MR 1607744 | Zbl 0910.54026
[6] Foertsch T., Schroeder V.: Products of hyperbolic metric spaces. Geom. Dedicata 102 (2003), 197–212. DOI 10.1023/B:GEOM.0000006539.14783.aa | MR 2026845
[7] Grzegrzolka P., Siegert J.: Boundaries of coarse proximity spaces and boundaries of compactifications. available at arXiv:1812.09802 [math.GN] (2020), 27 pages.
[8] Hartmann E.: Twisted coefficients on coarse spaces and their corona. available at arXiv:1904.00380 [math.MG] (2019), 14 pages.
[9] Hartmann E.: A pullback diagram in the coarse category. available at arXiv:1907.02961v1 [math.MG] (2019), 17 pages.
[10] Hartmann E.: Coarse cohomology with twisted coefficients. Math. Slovaca 70 (2020), no. 6, 1413–1444. DOI 10.1515/ms-2017-0440 | MR 4185787
[11] Kalantari S., Honari B.: Asymptotic resemblance. Rocky Mountain J. Math. 46 (2016), no. 4, 1231–1262. DOI 10.1216/RMJ-2016-46-4-1231 | MR 3563180
[12] Protasov I. V.: Normal ball structures. Mat. Stud. 20 (2003), no. 1, 3–16. MR 2019592 | Zbl 1053.54503
[13] Protasov I. V.: Coronas of balleans. Topology Appl. 149 (2005), no. 1–3, 149–160. DOI 10.1016/j.topol.2004.09.005 | MR 2130861 | Zbl 1068.54036
[14] Protasov I. V.: Coronas of ultrametric spaces. Comment. Math. Univ. Carolin. 52 (2011), no. 2, 303–307. MR 2849052 | Zbl 1240.54087
[15] Protasov I. V., Slobodianiuk S. V.: Ultrafilters on balleans. Ukraïn. Mat. Zh. 67 (2015), no. 12, 1698–1706; reprinted in Ukrainian Math. J. 67 (2016), no. 12, 1922–1931. MR 3541296
[16] Riehl E.: Category Theory in Context. Courier Dover Publications, Dover, 2017.
[17] Roe J.: Lectures on Coarse Geometry. University Lecture Series, 31, American Mathematical Society, Providence, 2003. DOI 10.1090/ulect/031/10 | MR 2007488 | Zbl 1042.53027
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