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Asymptotic dimension of finitely presented groups


Author: Thanos Gentimis
Journal: Proc. Amer. Math. Soc. 136 (2008), 4103-4110
MSC (2000): Primary 20F65, 20F69
DOI: https://doi.org/10.1090/S0002-9939-08-08973-9
Published electronically: July 17, 2008
MathSciNet review: 2431020
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Abstract: We prove that if a finitely presented group is one-ended, then its asymptotic dimension is greater than $ 1$. It follows that a finitely presented group of asymptotic dimension $ 1$ is virtually free.


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  • 1. A. Dranishnikov, Asymptotic topology, Russian Math. Surveys 55 (2000), No. 6, 1085-1129. MR 1840358 (2002j:55002)
  • 2. A. Dranishnikov and J. Smith, Asymptotic dimension of discrete groups, Fundamenta Mathematicae 189 (2006), No. 1, 27-34. MR 2213160 (2007h:20041)
  • 3. M. Dunwoody, The accessibility of finitely presented groups, Invent. Math. 81 (1985), No. 3, 449-457. MR 807066 (87d:20037)
  • 4. S. Gersten and Tim Riley, Filling length in finitely presentable groups, Geometriae Dedicata 92 (2002), 41-58. MR 1934008 (2003i:20051)
  • 5. M. Gromov, Hyperbolic groups, Essays in Group Theory (S. M. Gersten, ed.), MSRI Publ. 8, Springer-Verlag, 1987, pp. 75-263. MR 919829 (89e:20070)
  • 6. M. Gromov, Asymptotic invariants of infinite groups, Geometric Group Theory (G. Niblo, M. Roller, eds.), LMS Lecture Notes, vol. 182, Cambridge Univ. Press, 1993. MR 1253544 (95m:20041)
  • 7. T. Januszkiewicz and J. Swiatkowski, Filling Invariants in Systolic Complexes and Groups, preprint (June 2005).
  • 8. R. Lyndon and P. Schupp, Combinatorial Group Theory, Springer-Verlag, 1977. MR 0577064 (58:28182)
  • 9. J. Roe, Lectures on Coarse Geometry, Univ. Lect. Series, Vol. 31, Amer. Math. Society, 2003. MR 2007488 (2004g:53050)
  • 10. J-P. Serre, Trees, Springer-Verlag, 1980. MR 607504 (82c:20083)
  • 11. G. Yu, The Novikov conjecture for groups with finite asymptotic dimension, Ann. of Math. 147 (1998), No. 2, 325-355. MR 1626745 (99k:57072)

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Additional Information

Thanos Gentimis
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
Email: thanos@ufl.edu

DOI: https://doi.org/10.1090/S0002-9939-08-08973-9
Keywords: Dimension theory, asymptotic dimension, finitely presented group
Received by editor(s): August 15, 2005
Received by editor(s) in revised form: August 29, 2006
Published electronically: July 17, 2008
Additional Notes: Research supported by the program ’EPEAEK-Pythagoras’ (75% European grant, 25% Greek national grant)
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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