Algebraic & Geometric Topology

Coarse medians and Property A

Ján Špakula and Nick Wright

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Abstract

We prove that uniformly locally finite quasigeodesic coarse median spaces of finite rank and at most exponential growth have Property A. This offers an alternative proof of the fact that mapping class groups have Property A.

Article information

Source
Algebr. Geom. Topol., Volume 17, Number 4 (2017), 2481-2498.

Dates
Received: 15 July 2016
Accepted: 8 February 2017
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841448

Digital Object Identifier
doi:10.2140/agt.2017.17.2481

Mathematical Reviews number (MathSciNet)
MR3842848

Zentralblatt MATH identifier
06762696

Subjects
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 30L05: Geometric embeddings of metric spaces

Keywords
coarse median $CAT(0)$ cube complexes Yu's Property A

Citation

Špakula, Ján; Wright, Nick. Coarse medians and Property A. Algebr. Geom. Topol. 17 (2017), no. 4, 2481--2498. doi:10.2140/agt.2017.17.2481. https://projecteuclid.org/euclid.agt/1510841448


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References

  • J Behrstock, M,F Hagen, A Sisto, Hierarchically hyperbolic spaces, II: Combination theorems and the distance formula, preprint (2015)
  • J Behrstock, M,F Hagen, A Sisto, Asymptotic dimension and small-cancellation for hierarchically hyperbolic spaces and groups, Proc. Lond. Math. Soc. 114 (2017)
  • J Behrstock, M Hagen, A Sisto, Hierarchically hyperbolic spaces, I: Curve complexes for cubical groups, Geom. Topol. 21 (2017) 1731–1804
  • B,H Bowditch, Coarse median spaces and groups, Pacific J. Math. 261 (2013) 53–93
  • B,H Bowditch, Invariance of coarse median spaces under relative hyperbolicity, Math. Proc. Cambridge Philos. Soc. 154 (2013) 85–95
  • B,H Bowditch, Embedding median algebras in products of trees, Geom. Dedicata 170 (2014) 157–176
  • M,R Bridson, A Haefliger, Metric spaces of non-positive curvature, Grundl. Math. Wissen. 319, Springer (1999)
  • J Brodzki, S,J Campbell, E Guentner, G,A Niblo, N,J Wright, Property A and $\rm CAT(0)$ cube complexes, J. Funct. Anal. 256 (2009) 1408–1431
  • N,P Brown, N Ozawa, $C^*$–algebras and finite-dimensional approximations, Graduate Studies in Mathematics 88, Amer. Math. Soc., Providence, RI (2008)
  • M Gromov, Hyperbolic groups, from “Essays in group theory” (S,M Gersten, editor), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75–263
  • E Guentner, J Kaminker, Exactness and the Novikov conjecture, Topology 41 (2002) 411–418
  • U Hamenstädt, Geometry of the mapping class groups, I: Boundary amenability, Invent. Math. 175 (2009) 545–609
  • N Higson, J Roe, Amenable group actions and the Novikov conjecture, J. Reine Angew. Math. 519 (2000) 143–153
  • V,A Kaimanovich, Boundary amenability of hyperbolic spaces, from “Discrete geometric analysis” (M Kotani, T Shirai, T Sunada, editors), Contemp. Math. 347, Amer. Math. Soc., Providence, RI (2004) 83–111
  • Y Kida, Classification of the mapping class groups up to measure equivalence, Proc. Japan Acad. Ser. A Math. Sci. 82 (2006) 4–7
  • G,A Niblo, L,D Reeves, The geometry of cube complexes and the complexity of their fundamental groups, Topology 37 (1998) 621–633
  • P,W Nowak, Coarsely embeddable metric spaces without Property A, J. Funct. Anal. 252 (2007) 126–136
  • N Ozawa, Amenable actions and exactness for discrete groups, C. R. Acad. Sci. Paris Sér. I Math. 330 (2000) 691–695
  • M,A Roller, Poc sets, median algebras and group actions: an extended study of Dunwoody's construction and Sageev's theorem, preprint (1998) Available at \setbox0\makeatletter\@url http://www.personal.soton.ac.uk/gan/Roller.pdf {\unhbox0
  • R Willett, Some notes on property A, from “Limits of graphs in group theory and computer science” (G Arzhantseva, A Valette, editors), EPFL Press, Lausanne (2009) 191–281
  • G Yu, The coarse Baum–Connes conjecture for spaces which admit a uniform embedding into Hilbert space, Invent. Math. 139 (2000) 201–240