By W. J. Harvey, C. Maclachlan

ISBN-10: 0511565798

ISBN-13: 9780511565793

ISBN-10: 0521429323

ISBN-13: 9780521429320

This quantity includes a choice of refereed papers offered in honour of A.M. Macbeath, one of many best researchers within the quarter of discrete teams. the topic has been of a lot present curiosity of overdue because it consists of the interplay of a few diversified issues equivalent to team conception, hyperbolic geometry, and complicated research.

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**Additional resources for Discrete Groups and Geometry**

**Example text**

PROPOSITION 3. Suppose that, for all subgraphs A of T such that C& is finite, \CA\ is invertible in R. Then Cr G FP(R), and where the sum is over all subgraphs A of T such that C& is finite. (Here \A\ means the number of vertices of A, the empty subgraph is allowed as a subgraph and C$ is the trivial group). PROOF. According to ยง14 in [10], there is a contractible Cr-complex Y on which Cr acts properly. The quotient Y/Cr is a simplicial complex, in which an r-simplex is of the form 0 C Ao CAx C .

Math. Rep. Acad. Sci. 2 (1981) 99-103. M. ElCHLER. Lectures on Modular Correspondences, Tata Institute (1955-6), (1965). T. ESTERMANN. A new application of the Hardy-LittlewoodKloostermann method. Proc. London Math. Soc. (3) 12 (1962) 425-444. D. HEJHAL. 1, Springer Lecture Notes, 548. Pell equations and Fuchsian groups 35 [9] G. HUMBERT. Comptes Rendus 166 (1918) 753, 171 (1920) 287,377. [10] H. IWANIEC. Spectral Theory of Auto morphia Functions Part I. 12. [11] E. LANDAU. J. Nachr. Ges. d. Wiss.

In: Low-dimensional topology and Kleinian groups, (ed. Epstein), London Math. Soc. Lecture Notes 111 297-304. Cambridge: University Press 1986. 46 Chiswell [8] I. M. Chiswell, D. J. Collins and J. Huebschmann, "Aspherical group presentations", Math. Z. 178 (1981), 1-36. [9] H. S. M. Coxeter and W. 0. J. Moser, Generators and relations for discrete groups. Berlin, Heidelberg: Springer-Verlag 1980. [10] M. W. Davis, "Groups generated by reflections and aspherical manifolds not covered by Euclidean space", Annals of Math.

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