Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Relating exponential growth in a manifold and its fundamental group


Author: Anthony Manning
Journal: Proc. Amer. Math. Soc. 133 (2005), 995-997
MSC (2000): Primary 20F69, 37D40; Secondary 20F65, 37B40
DOI: https://doi.org/10.1090/S0002-9939-04-07755-X
Published electronically: October 14, 2004
MathSciNet review: 2117199
Full-text PDF Free Access

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 [Enhancements On Off] (What's this?)

  • 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: https://doi.org/10.1090/S0002-9939-04-07755-X
Received by editor(s): December 10, 2003
Published electronically: October 14, 2004
Communicated by: Michael Handel
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society