Abstract
The growth function of the fundamental group of an orientable surface of genusg≥2 is computed via rewriting systems and a formula due to R. I. Grigorchuk.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. I. Grigorchuk, “On growth in group theory,”Proceedings of the ICM Kyoto 90,1, 325–338 (1990).
J. W. Cannon,The Growth of the Closed Groups of Surfaces and the Compact Hyperbolic Groups, Preprint, Boston (1979).
R. I. Grigorchuk, “Growth functions, rewriting systems, and the Euler characteristic,”Mat. Zametki [Math. Notes],58, No. 5, 653–668 (1995).
M. Stoll,Some Group Presentations with Rational Growth, Preprint, Boston (1994).
D. E. Cohen, “String rewriting: a survey for group theorists,” in:Geometric Group Theory, Vol. 1, Sussex (1991);London Math. Soc. Lect. Note Series,181, 37–47 (1993).
D. B. A. Epstein, J. W. Cannon, D. F. Holt, S. V. F. Levy, M. S. Paterson, and W. P. Thurston,Word Processing in Groups, Jones and Bartlett, Boston (1992).
N. Bourbaki,Groupes et algèbres de Lie, Hermann, Paris (1968).
Additional information
Translated fromMatematicheskie Zametki, Vol. 58, No. 5, pp. 681–693, November, 1995.
The author is deeply indebted to R. I. Grigorchuk for setting the problem and useful discussions.
This research was partially supported by the Ministry of Culture and Science of the Islamic Republic of Iran.
Rights and permissions
About this article
Cite this article
Mamagani, M.D. Growth functions of groups of surfaces. Math Notes 58, 1156–1165 (1995). https://doi.org/10.1007/BF02304999
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02304999