A COARSELY INVARIANT NOTION OF ROUNDNESS

Year 2015, Volume: 8 Issue: 2, 154 - 167, 30.10.2015

Alexander Basyrov Matthew Horak

https://doi.org/10.36890/iejg.592303

Abstract

Keywords

Coarse embedding, uniform embedding, Hilbert space, roundness

References

• [1] Dranishnikov, A.N., Gong, G., Lafforgue, V., and Yu, G. Uniform embeddings into hilbert space and a question of gromov, Canadian Mathematical Bulletin, 45(2002), no. 1, 60–70.
• [2] Enflo, P., On a problem of Smirnov, Arkiv f¨or Matematik, 8 (1970), no. 2, 107–109.
• [3] Ferry, S.C., Ranicki, A. and Rosenberg, J., Novikov conjectures, index theorems and rigidity: Oberwolfach 1993, vol. 1, Cambridge Univ Pr, 1995.
• [4] Gromov, M., Geometric group theory, Asymptotic invariants of infinite groups, vol. 2, Cam- bridge University Press, vol. 182, 1993.
• [5] Lafont, J.F., and Prassidis, S., Roundness properties of groups, Geometriae Dedi- cata,117(2006), no. 1, 137–160.
• [6] Lennard, C.J., Tonge, A.M., and Weston, A., Generalized roundness and negative type, Michigan Math. J, 44(1997), no. 1, 37–45.
• [7] Nowak, P.W., Coarse embeddings of metric spaces into banach spaces, Proceedings of the American Mathematical Society, 133(2005), no. 9, 2589–2596.
• [8] Ostrovskii, M.I., Coarse embeddability into Banach spaces, Topology Proc., 33 (2009), 163– 183.
• [9] Ostrovskii, M.I., Expansion properties of metric spaces not admitting a coarse embedding into a Hilbert space, C. R. Acad. Bulgare Sci. 62(2009), no. 4, 415–420.
• [10] Roe, J., Lectures on coarse geometry, Amer Mathematical Society, vol. 31, 2003.
• [11] Yu, G., The coarse baum–connes conjecture for spaces which admit a uniform embedding into hilbert space, Inventiones Mathematicae, 139(2000), no. 1, 201–240.