Algebraic & Geometric Topology Volume 13, issue 2 (2013)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Cofinite hyperbolic Coxeter groups, minimal growth rate and Pisot numbers

Ruth Kellerhals

Algebraic & Geometric Topology 13 (2013) 1001–1025

DOI: 10.2140/agt.2013.13.1001

Bibliography

1	R Charney, M Davis, Reciprocity of growth functions of Coxeter groups, Geom. Dedicata 39 (1991) 373 MR1123152
2	H S M Coxeter, Discrete groups generated by reflections, Ann. of Math. 35 (1934) 588 MR1503182
3	H S M Coxeter, W O J Moser, Generators and relations for discrete groups, Ergeb. Math. Grenzgeb. 14, Springer (1980) MR562913
4	W J Floyd, Growth of planar Coxeter groups, P V numbers, and Salem numbers, Math. Ann. 293 (1992) 475 MR1170521
5	P de la Harpe, Groupes de Coxeter infinis non affines, Exposition. Math. 5 (1987) 91 MR880259
6	E Hironaka, The Lehmer polynomial and pretzel links, Canad. Math. Bull. 44 (2001) 440 MR1863636
7	N W Johnson, R Kellerhals, J G Ratcliffe, S T Tschantz, The size of a hyperbolic Coxeter simplex, Transform. Groups 4 (1999) 329 MR1726696
8	I M Kaplinskaja, The discrete groups that are generated by reflections in the faces of simplicial prisms in Lobačevskiĭspaces, Mat. Zametki 15 (1974) 159 MR0360858
9	R Kellerhals, A Kolpakov, The minimal growth rate of cocompact Coxeter groups in hyperbolic 3–space, to appear in Canadian J. Math.
10	R Kellerhals, G Perren, On the growth of cocompact hyperbolic Coxeter groups, European J. Combin. 32 (2011) 1299 MR2838016
11	A Kolpakov, Deformation of finite-volume hyperbolic Coxeter polyhedra, limiting growth rates and Pisot numbers, European J. Combin. 33 (2012) 1709 MR2950475
12	Y Komori, Y Umemoto, The growth functions of noncompact 3–dimensional hyperbolic Coxeter groups with 4 and 5 generators, preprint (2012)
13	Y Komori, Y Umemoto, On the growth of hyperbolic 3–dimensional generalized simplex reflection groups, Proc. Japan Acad. Ser. A Math. Sci. 88 (2012) 62 MR2912844
14	J L Koszul, Lectures on hyperbolic Coxeter groups, lecture notes, University of Notre Dame (1967)
15	R Meyerhoff, The cusped hyperbolic 3–orbifold of minimum volume, Bull. Amer. Math. Soc. 13 (1985) 154 MR799800
16	W Parry, Growth series of Coxeter groups and Salem numbers, J. Algebra 154 (1993) 406 MR1206129
17	J Rotman, Galois theory, Universitext, Springer (1998) MR1645586
18	C J Smyth, On the product of the conjugates outside the unit circle of an algebraic integer, Bull. London Math. Soc. 3 (1971) 169 MR0289451
19	L Solomon, The orders of the finite Chevalley groups, J. Algebra 3 (1966) 376 MR0199275
20	R Steinberg, Endomorphisms of linear algebraic groups, Memoirs of the American Mathematical Society 80, American Mathematical Society (1968) 108 MR0230728
21	È B Vinberg, Hyperbolic groups of reflections, Uspekhi Mat. Nauk 40 (1985) 29, 255 MR783604
22	È B Vinberg, O V Shvartsman, Discrete groups of motions of spaces of constant curvature, from: "Geometry, II", Encyclopaedia Math. Sci. 29, Springer (1993) 139 MR1254933
23	T Zehrt, C Zehrt-Liebendörfer, The growth function of Coxeter garlands in $\mathbb{H}^4$, Beitr. Algebra Geom. 53 (2012) 451 MR2971753