|
Relating exponential growth in a manifold and its fundamental group
Author(s):
Anthony
Manning
Journal:
Proc. Amer. Math. Soc.
133
(2005),
995-997.
MSC (2000):
Primary 20F69, 37D40;
Secondary 20F65, 37B40
Posted:
October 14, 2004
MathSciNet review:
2117199
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We relate the growth rate of volume in the universal cover of a compact Riemannian manifold to the growth in the fundamental group in terms of word length in a given set of generators and the length of geodesics representing these generators.
References:
-
- 1.
- L. Bartholdi, A Wilson group of non-uniformly exponential growth, C. R. Math. Acad. Sci. Paris 336 (2003), no. 7, 549-554. MR 1981466 (2004c:20051)
- 2.
- M. Gromov, Metric structures for Riemannian and non-Riemannian spaces, Progress in Mathematics, 152. Birkhäuser Boston, Inc., Boston, MA, 1999. MR 1699320 (2000d:53065)
- 3.
- P. de la Harpe, Topics in geometric group theory, Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 2000. MR 1786869 (2001i:20081)
- 4.
- -, Uniform growth in groups of exponential growth, Geom. Dedicata 95 (2002), 1-17. MR 1950882 (2003k:20031)
- 5.
- A. Katok and B. Hasselblatt, Introduction to the modern theory of dynamical systems, Encyclopedia of Mathematics and its Applications, 54. Cambridge University Press, Cambridge, 1995. MR 1326374 (96c:58055)
- 6.
- A. Manning, Topological entropy for geodesic flows, Ann. of Math. (2), 110 (1979), no. 3, 567-573. MR 0554385 (81e:58044)
- 7.
- D. Osin, The entropy of solvable groups, Ergodic Theory Dynam. Systems 23 (2003), no. 3, 907-918. MR 1992670 (2004f:20065)
- 8.
- G. Paternain, Geodesic flows, Progress in Mathematics, 180. Birkhäuser Boston, Inc., Boston, MA, 1999. MR 1712465 (2000h:53108)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
20F69, 37D40,
20F65, 37B40
Retrieve articles in all Journals with
MSC (2000):
20F69, 37D40,
20F65, 37B40
Additional Information:
Anthony
Manning
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
Email:
akm@maths.warwick.ac.uk
DOI:
10.1090/S0002-9939-04-07755-X
PII:
S 0002-9939(04)07755-X
Received by editor(s):
December 10, 2003
Posted:
October 14, 2004
Communicated by:
Michael Handel
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
