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On the semisimplicity of polyhedral isometries
Author(s):
Martin
R.
Bridson
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2143-2146.
MSC (1991):
Primary 53C23, 20F32
Posted:
March 16, 1999
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Abstract:
If a polyhedral complex  has only finitely many isometry types of cells, then all of its cellular isometries are semisimple. If  is 1-connected and non-positively curved, then any solvable group that acts freely by cellular isometries on  is finitely generated and contains an abelian subgroup of finite index.
References:
- [B]
- M.R. Bridson, Geodesics and curvature in metric simplicial complexes, Group Theory From a Geometrical Viewpoint (E. Ghys, A. Haefliger, A. Verjovsky, ed.), World Scientific, 1991, pp. 373-463. MR 94c:57040
- [BH]
- M.R. Bridson and A. Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin-Heidelberg-New York, 1999.
- [BM]
- M. Burger and S. Mozes, CAT(-1) spaces, divergence groups and their commensurators, J. Amer. Math. Soc. 9 (1996), 57-93. MR 96c:20065
- [BS]
- W. Ballmann and J. \'{S}wi[??]atkowski, On groups which act on cube complexes, preprint, 1998.
- [GW]
- D. Gromoll and J. Wolf, Some relations between the metric structure and the algebraic structure of the fundamental group in manifolds of nonpositive curvature, Bull. Amer. Math. Soc. 77 (1971), 545-552. MR 43:6841
- [G1]
- M. Gromov, Hyperbolic groups, Essays in group theory (S.M. Gersten, ed.), MSRI Publication 8, Springer-Verlag, New York, 1988, pp. 75-263. MR 89e:20070
- [G2]
- M. Gromov, Hyperbolic manifolds, groups and actions, Riemann Surfaces and related Topics (Stony Brook, 1978), Ann. of Math. Studies, vol. 97, Princeton Univ. Press, 1981, pp. 183-213.
- [LY]
- H. B. Lawson and S. T. Yau, Compact manifolds of nonpositive curvature, J. Diff. Geom. 7 (1972), 211-228. MR 48:12402
- [M]
- G. A. Margulis, Discrete subgroups of Lie groups, Ergebnisse der Math., Springer-Verlag, Berlin-Heidelberg-New York, 1990.
- [Se]
- D. Segal, Polycyclic groups, Camb. Univ. Press, 1985. MR 85h:20003
- [Sr]
- J-P. Serre, Trees, Springer-Verlag, Berlin-Heidelberg-New York, 1980. MR 82c:20083
- [Z]
- R. Zimmer, Ergodic Theory and Semisimple Groups, Monog. Math., Vol 81, Birkhäuser, Basel, 1984. MR 86j:22014
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Additional Information:
Martin
R.
Bridson
Affiliation:
Mathematical Institute, 24--29 St Giles', Oxford, OX1 3LB, United Kingdom
Email:
bridson@maths.ox.ac.uk
DOI:
10.1090/S0002-9939-99-05187-4
PII:
S 0002-9939(99)05187-4
Keywords:
Non-positive curvature,
semisimple isometries
Received by editor(s):
October 7, 1997
Posted:
March 16, 1999
Additional Notes:
This work was supported by an EPSRC Advanced Fellowship, NSF grant 9401362 and the British Council
Communicated by:
Ronald M. Solomon
Copyright of article:
Copyright
1999,
American Mathematical Society
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