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Hyperbolic groups have finite asymptotic dimension
Author(s):
John
Roe
Journal:
Proc. Amer. Math. Soc.
133
(2005),
2489-2490.
MSC (2000):
Primary 20F67;
Secondary 55M10
Posted:
April 8, 2005
MathSciNet review:
2146189
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Abstract:
We detail a proof of a result of Gromov, that hyperbolic groups (and metric spaces) have finite asymptotic dimension. This fact has become important in recent work on the Novikov conjecture.
References:
-
- 1.
- M. Bonk and O. Schramm, Embeddings of Gromov hyperbolic spaces, Geometric and Functional Analysis 10 (2000), 266-306. MR 1771428 (2001g:53077)
- 2.
- E. Ghys and P. de la Harpe, Sur les groupes hyperboliques d'après Mikhael Gromov, Progress in Mathematics, vol. 83, Birkhäuser, Boston, 1990. MR 1086648 (92f:53050)
- 3.
- M. Gromov, Hyperbolic groups, Essays in Group Theory (S.M. Gersten, ed.), Springer-Verlag, New York-Heidelberg-Berlin, 1987, Mathematical Sciences Research Institute Publications 8, pp. 75-263. MR 0919829 (89e:20070)
- 4.
- -, Asymptotic invariants for infinite groups, Geometric Group Theory (G.A. Niblo and M.A. Roller, eds.), LMS Lecture Notes, vol. 182, Cambridge University Press, Cambridge, 1993, pp. 1-295. MR 1253544 (95m:20041)
- 5.
- G. Yu, The Novikov conjecture for groups with finite asymptotic dimension, Annals of Mathematics 147 (1998), 325-355. MR 1626745 (99k:57072)
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Additional Information:
John
Roe
Affiliation:
Department of Mathematics, Penn State University, University Park, Pennsylvania 16802
Email:
roe@math.psu.edu
DOI:
10.1090/S0002-9939-05-08138-4
PII:
S 0002-9939(05)08138-4
Keywords:
Gromov hyperbolicity,
coarse geometry,
asymptotic dimension
Received by editor(s):
May 1, 2002
Posted:
April 8, 2005
Additional Notes:
The author was supported in part by NSF Grant \#0100464.
Communicated by:
Mohan Ramachandran
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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