The asymptotic dimension of quotients by finite groups
HTML articles powered by AMS MathViewer
- by Daniel Kasprowski PDF
- Proc. Amer. Math. Soc. 145 (2017), 2383-2389 Request permission
Abstract:
Let $X$ be a proper metric space and let $F$ be a finite group acting on $X$ by isometries. We show that the asymptotic dimension of $F\backslash X$ is the same as the asymptotic dimension of $X$.References
- Arthur Bartels and David Rosenthal, On the $K$-theory of groups with finite asymptotic dimension, J. Reine Angew. Math. 612 (2007), 35–57. MR 2364073, DOI 10.1515/CRELLE.2007.083
- A. N. Dranishnikov, Asymptotic topology, Uspekhi Mat. Nauk 55 (2000), no. 6(336), 71–116 (Russian, with Russian summary); English transl., Russian Math. Surveys 55 (2000), no. 6, 1085–1129. MR 1840358, DOI 10.1070/rm2000v055n06ABEH000334
- Martin Finn-Sell and Jianchao Wu, The asymptotic dimension of box spaces for elementary amenable groups, arXiv:1508.05018v1.
- M. Gromov, Asymptotic invariants of infinite groups, Geometric group theory, Vol. 2 (Sussex, 1991) London Math. Soc. Lecture Note Ser., vol. 182, Cambridge Univ. Press, Cambridge, 1993, pp. 1–295. MR 1253544
- Daniel Kasprowski, On the $K$-theory of linear groups, Ann. K-Theory 1 (2016), no. 4, 441–456. MR 3536434, DOI 10.2140/akt.2016.1.441
- Takahisa Miyata and Žiga Virk, Dimension-raising maps in a large scale, Fund. Math. 223 (2013), no. 1, 83–97. MR 3125134, DOI 10.4064/fm223-1-6
- A. R. Pears, Dimension theory of general spaces, Cambridge University Press, Cambridge, England-New York-Melbourne, 1975. MR 0394604
- John Roe, Lectures on coarse geometry, University Lecture Series, vol. 31, American Mathematical Society, Providence, RI, 2003. MR 2007488, DOI 10.1090/ulect/031
Additional Information
- Daniel Kasprowski
- Affiliation: Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
- MR Author ID: 1081473
- Email: kasprowski@mpim-bonn.mpg.de
- Received by editor(s): May 31, 2016
- Received by editor(s) in revised form: August 1, 2016
- Published electronically: December 15, 2016
- Communicated by: Ken Bromberg
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 2383-2389
- MSC (2010): Primary 20F69, 54F45, 55M10
- DOI: https://doi.org/10.1090/proc/13491
- MathSciNet review: 3626497