Growth functions on Fuchsian groups and the Euler characteristic

DOI10.1007/BF01405088zbMath0608.20036OpenAlexW2095896857MaRDI QIDQ1086358

Steven P. Plotnick, William J. Floyd

Publication date: 1987

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143441

zbMATH Keywords

growth seriesgrowth functionsfinitely generated grouprational Euler characteristicfinite generating setcompact hyperbolic Coxeter groupEuclidean Coxeter groupword norm

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Homological methods in group theory (20J05) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Fundamental group, presentations, free differential calculus (57M05) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

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Cites Work

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• Groups generated by reflections and aspherical manifolds not covered by Euclidean space
• Infinite Eulerian tessellations
• Growth functions and Euler series
• The combinatorial structure of cocompact discrete hyperbolic groups
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• A note on curvature and fundamental group
• Growth of finitely generated solvable groups
• Growth of finitely generated solvable groups and curvature of Riemannian manifolds
• On Poincaré's theorem for fundamental polygons
• Forcing in intuitionistic systems without power-set
• Counterexamples Involving Growth Series and Euler Characteristics
• The Degree of Polynomial Growth of Finitely Generated Nilpotent Groups