Journal of East China Normal University(Natural Science) >

2022 , Vol. 2022 >Issue 6: 44 - 53

DOI: https://doi.org/10.3969/j.issn.1000-5641.2022.06.006

Mathematics

Finite coarse asymptotic property C-decomposition complexity

  • Guoqiang LI
Expand
  • School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang　550025, China

Received date: 2021-03-23

  Online published: 2022-11-22

Fold

Abstract

This paper establishes a coarse version of finite asymptotic property C-decomposition complexity in the context of coarse spaces. In particular, permanence properties of finite asymptotic property C-decomposition complexity are studied, and it is shown that finite coarse asymptotic property C-decomposition complexity implies coarse property A. In addition, the paper explores coarse property C and coarse decomposition complexity.

Key words： coarse geometry; finite asymptotic property C-decomposition complexity; property A; asymptotic property C; finite decomposition complexity

Cite this article

Guoqiang LI . Finite coarse asymptotic property C-decomposition complexity[J]. Journal of East China Normal University(Natural Science), 2022 , 2022(6) : 44 -53 . DOI: 10.3969/j.issn.1000-5641.2022.06.006

References

1 BELL G, GLODKOWSKI D, NAGORKO A. Decomposition theorems for asymptotic property C and property A. Topology and its Applications, 2019, 256, 248- 261.
2 DRANISHNIKOV A, ZARICHNYI M. Remarks on straight finite decomposition complexity. Topology and its Applications, 2017, 227, 102- 110.
3 YAMAUCHI T. Asymptotic property C of the countable direct sum of the integers. Topology and its Applications, 2015, 184, 50- 53.
4 YU G L. The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space. Inventiones Mathematicae, 2000, 139, 201- 240.
5 REO J. Lectures on Coarse Geometry [M]. Providence, America: American Mathematical Society, 2003.
6 GROMOV M. Asymptotic Invariants of Infinite Groups [M]. Cambridge: Cambridge University Press, 1993.
7 BELL G, MORAN D, NAGORKO A. Coarse property C and decomposition complexity. Topology and its Applications, 2017, 227, 30- 50.
8 GUENTNER E, TESSERA R, YU G L. A notion of geometric complexity and its application to topological rigidity. Inventiones Mathematicae, 2012, 189, 315- 357.
9 GUENTNER E, TESSERA R, YU G L. Discrete groups with finite decomposition complexity. Groups Geometry and Dynamics, 2013, 7 (2): 377- 402.
10 DRANISHNIKOV A N. Asymptotic topology. Russian Mathematical Surveys, 1999, 55 (6): 71- 116.
11 GRAVE B. Coarse geometry and asymptotic dimension [D]. Gottingen: University of Gottingen, 2005.
12 WILLETT R. Some notes on property A [EB/OL]. (2008-05-09)[2021-01-20]. https://arxiv.org/pdf/math/0612492.pdf.
Options
Outlines

/

〈 〉