Counterexamples involving growth series and Euler characteristics
HTML articles powered by AMS MathViewer
- by Walter Parry PDF
- Proc. Amer. Math. Soc. 102 (1988), 49-51 Request permission
Abstract:
This note presents examples for which the value of a finitely generated group’s growth series at 1 is not the reciprocal of the group’s Euler characteristic.References
- M. Benson, Growth series of finite extensions of $\textbf {Z}^{n}$ are rational, Invent. Math. 73 (1983), no. 2, 251–269. MR 714092, DOI 10.1007/BF01394026
- N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
- James W. Cannon, The combinatorial structure of cocompact discrete hyperbolic groups, Geom. Dedicata 16 (1984), no. 2, 123–148. MR 758901, DOI 10.1007/BF00146825 —, The growth of the closed surface groups and the compact hyperbolic Coxeter groups, preprint.
- William J. Floyd and Steven P. Plotnick, Growth functions on Fuchsian groups and the Euler characteristic, Invent. Math. 88 (1987), no. 1, 1–29. MR 877003, DOI 10.1007/BF01405088 M. Grayson, Geometry and growth in three dimensions, Ph.D. Thesis, Princeton Univ., 1983.
- Jean-Pierre Serre, Cohomologie des groupes discrets, Prospects in mathematics (Proc. Sympos., Princeton Univ., Princeton, N.J., 1970) Ann. of Math. Studies, No. 70, Princeton Univ. Press, Princeton, N.J., 1971, pp. 77–169 (French). MR 0385006
- N. Smythe, Growth functions and Euler series, Invent. Math. 77 (1984), no. 3, 517–531. MR 759259, DOI 10.1007/BF01388836
- Philip Wagreich, The growth function of a discrete group, Group actions and vector fields (Vancouver, B.C., 1981) Lecture Notes in Math., vol. 956, Springer, Berlin, 1982, pp. 125–144. MR 704992, DOI 10.1007/BFb0101514
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 102 (1988), 49-51
- MSC: Primary 20F05
- DOI: https://doi.org/10.1090/S0002-9939-1988-0915713-7
- MathSciNet review: 915713