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Two-dimensional systolic complexes satisfy property A by:1 (Source: Crossref)

    We show that two-dimensional systolic complexes are quasi-isometric to quadric complexes with flat intervals. We use this fact along with the weight function of Brodzki, Campbell, Guentner, Niblo and Wright [J. Brodzki, S. J. Campbell, E. Guentner, G. A. Niblo and N. J. Wright, Property A and CAT(0) cube complexes, J. Funct. Anal.256(5) (2009) 1408–1431] to prove that two-dimensional systolic complexes satisfy property A.

    Communicated by A. Ol’shanskii

    AMSC: 20F65, 20F69, 57M20


    • 1. S. Adams , Boundary amenability for word hyperbolic groups and an application to smooth dynamics of simple groups, Topology 33(4) (1994) 765–783. Google Scholar
    • 2. W. Ballmann and J. Świa̧tkowski , On L2-cohomology and property (T) for automorphism groups of polyhedral cell complexes, Geom. Funct. Anal. 7(4) (1997) 615–645. ISIGoogle Scholar
    • 3. H.-J. Bandelt , Hereditary modular graphs, Combinatorica 8(2) (1988) 149–157. ISIGoogle Scholar
    • 4. M. Bridson and A. Haefliger , Metric Spaces of Non-Positive Curvature, Vol. 319 (Springer, 1999). Google Scholar
    • 5. J. Brodzki, S. J. Campbell, E. Guentner, G. A. Niblo and N. J. Wright , Property A and CAT(0) cube complexes, J. Funct. Anal. 256(5) (2009) 1408–1431. ISIGoogle Scholar
    • 6. S. J. Campbell , Property A and affine buildings, J. Funct. Anal. 256(2) (2009) 409–431. ISIGoogle Scholar
    • 7. S. J. Campbell and G. A. Niblo , Hilbert space compression and exactness of discrete groups, J. Funct. Anal. 222(2) (2005) 292–305. ISIGoogle Scholar
    • 8. V. Chepoi , Graphs of some CAT(0) complexes, Adv. Appl. Math. 24(2) (2000) 125–179. ISIGoogle Scholar
    • 9. A. Hatcher , Algebraic Topology (Cambridge University Press, Cambridge, 2002). Google Scholar
    • 10. N. Higson and J. Roe , Amenable group actions and the Novikov conjecture, J. Reine Angew. Math. 519 (2000) 143–153. ISIGoogle Scholar
    • 11. N. Hoda, Quadric complexes, arXiv:1711.05844 [math.GR]. Google Scholar
    • 12. T. Januszkiewicz and J. Świa̧tkowski , Simplicial nonpositive curvature, Publ. Math. Inst. Hautes Études Sci. 104(1) (2006) 1–85. ISIGoogle Scholar
    • 13. R. C. Lyndon and P. E. Schupp , Combinatorial Group Theory, Classics in Mathematics (Springer-Verlag, Berlin, 2001) [Reprint of the 1977 edition]. Google Scholar
    • 14. N. Ozawa , Amenable actions and exactness for discrete groups, C. R. Acad. Sci. Paris Sér. I, Math. 330(8) (2000) 691–695. Google Scholar
    • 15. D. T. Wise, Sixtolic complexes and their fundamental groups, preprint (2003). Google Scholar
    • 16. G. Yu , The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space, Invent. Math. 139(1) (2000) 201–240. ISIGoogle Scholar
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