Proceedings of the American Mathematical Society

Author(s): Mark Pollicott; Richard Sharp
Journal: Proc. Amer. Math. Soc. 124 (1996), 1329-1335.
MSC (1991): Primary 20F05, 58F15
Retrieve article in: PDF
This article is available free of charge

Abstract: In this paper we study growth series associated to commutator subgroups of surface groups. We conclude that these growth series are not rational.

1.: J. Cannon, The combinatorial structure of co-compact discrete hyperbolic groups, Geom. Dedicata 16 (1984), 123-148. MR 86j:20032
2.: W. Floyd and S. Plotnick, Growth functions on Fuchsian groups and the Euler characteristic, Invent. math. 88 (1987), 1-29. MR 88m:22023
3.: F. R. Gantmacher, The Theory of Matrices, Vol. II, Chelsea, New York, 1974. MR 21:6372c (earlier ed.)
4.: M. Gromov, Hyperbolic groups, MSRI publications, Vol. 8 (S. Gersten, ed.), Springer, Berlin, 1987, pp. 75--263. MR 89e:20070
5.: W. Parry, Counterexamples involving growth series and the Euler characteristic, Proc. Amer. Math. Soc. 102 (1988), 49--51. MR 89c:20051
6.: M. Pollicott and R. Sharp, Rates of recurrence for $\mathbb{Z}^{q}$ and $\mathbb{R}^{q}$ extensions of subshifts of finite type, J. London Math. Soc. 49 (1994), 401-416. MR 95f:54037
7.: C. Series, Symbolic dynamics for geodesic flows, Acta Mathematica 146 (1981), 103-128. MR 82f:58071
8.: N. Varopoulos, L. Saloff-Coste and T. Coulhon, Analysis and Geometry on Groups, Cambridge University Press, Cambridge, 1992. MR 95f:43008

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 20F05, 58F15

Mark Pollicott
Affiliation: Department of Mathematics, Warwick University, Coventry, CV4 7AL, England
Address at time of publication: Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, England

Richard Sharp
Affiliation: School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London, E1 4NS, England
Address at time of publication: Department of Mathematics, University of Manchester, Oxford Road, Man- chester M13 9PL, England

DOI: 10.1090/S0002-9939-96-03362-X
PII: S 0002-9939(96)03362-X
Received by editor(s): April 1, 1994
Additional Notes: The first author was supported by The Royal Society through a University Research Fellowship.
The second author was supported by the UK SERC under grant number GR/G51930.
Dedicated: Dedicated to William Parry on the occasion of his 60th birthday
Communicated by: Ronald M. Solomon
Copyright of article: Copyright 1996, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS