asymptotic dimension

Related nnLab entries: dimension, coarse topology

  • Mikhail Gromov, Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ. 8, Springer, New York, 1987, pp. 75–263. MR MR919829 (89e:20070) 61; Asymptotic invariants of infinite groups, in: Geometric group theory, vol. 2 (Sussex, 1991), London Math. Soc. Lecture Note Ser. 182, Cambridge Univ. Press 1993, pp. 1–295. MR1253544 (95m:20041)

  • G. Bell, A. Dranishnikov, Asymptotic dimension, math.GR/0703766

The asymptotic dimension theory was founded by Gromov in the early 90s. In this paper we give a survey of its recent history where we emphasize two of its features: an analogy with the dimension theory of compact metric spaces and applications to the theory of discrete groups.

  • B. Grave, Asymptotic dimension of coarse spaces, New York J. Math. 12 (2006) 249–256
category: topology

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