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Coxeter systems with $2$–dimensional Davis complexes, growth rates and Perron numbers

Naomi Bredon and Tomoshige Yukita

Algebraic & Geometric Topology 24 (2024) 1787–1808
Bibliography
1 M J Bertin, A Decomps-Guilloux, M Grandet-Hugot, M Pathiaux-Delefosse, J P Schreiber, Pisot and Salem numbers, Birkhäuser (1992) MR1187044
2 R Charney, M Davis, Reciprocity of growth functions of Coxeter groups, Geom. Dedicata 39 (1991) 373 MR1123152
3 M W Davis, The geometry and topology of Coxeter groups, 32, Princeton Univ. Press (2008) MR2360474
4 A Felikson, P Tumarkin, Reflection subgroups of Coxeter groups, Trans. Amer. Math. Soc. 362 (2010) 847 MR2551508
5 W J Floyd, Growth of planar Coxeter groups, PV numbers, and Salem numbers, Math. Ann. 293 (1992) 475 MR1170521
6 K Fujiwara, Z Sela, The rates of growth in a hyperbolic group, Invent. Math. 233 (2023) 1427 MR4623546
7 J A Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 1998 (1998) MR1668059
8 R I Grigorchuk, Degrees of growth of finitely generated groups and the theory of invariant means, Izv. Akad. Nauk SSSR Ser. Mat. 48 (1984) 939 MR0764305
9 M Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981) 53 MR0623534
10 P de la Harpe, Groupes de Coxeter infinis non affines, Expo. Math. 5 (1987) 91 MR0880259
11 J E Humphreys, Reflection groups and Coxeter groups, 29, Cambridge Univ. Press (1990) MR1066460
12 R Kellerhals, G Perren, On the growth of cocompact hyperbolic Coxeter groups, European J. Combin. 32 (2011) 1299 MR2838016
13 A Kolpakov, Deformation of finite-volume hyperbolic Coxeter polyhedra, limiting growth rates and Pisot numbers, European J. Combin. 33 (2012) 1709 MR2950475
14 Y Komori, T Yukita, On the growth rate of ideal Coxeter groups in hyperbolic 3–space, Proc. Japan Acad. Ser. A Math. Sci. 91 (2015) 155 MR3430205
15 C T McMullen, Coxeter groups, Salem numbers and the Hilbert metric, Publ. Math. Inst. Hautes Études Sci. 95 (2002) 151 MR1953192
16 J R Munkres, Elements of algebraic topology, Addison-Wesley (1984) MR0755006
17 J Nonaka, R Kellerhals, The growth rates of ideal Coxeter polyhedra in hyperbolic 3–space, Tokyo J. Math. 40 (2017) 379 MR3743725
18 W Parry, Growth series of Coxeter groups and Salem numbers, J. Algebra 154 (1993) 406 MR1206129
19 J G Ratcliffe, Foundations of hyperbolic manifolds, 149, Springer (1994) MR1299730
20 L Solomon, The orders of the finite Chevalley groups, J. Algebra 3 (1966) 376 MR0199275
21 R Steinberg, Endomorphisms of linear algebraic groups, 80, Amer. Math. Soc. (1968) 108 MR0230728
22 T Terragni, On the growth of a Coxeter group, Groups Geom. Dyn. 10 (2016) 601 MR3513110
23 J A Wolf, Growth of finitely generated solvable groups and curvature of Riemannian manifolds, J. Differential Geom. 2 (1968) 421 MR0248688
24 T Yukita, On the growth rates of cofinite 3–dimensional hyperbolic Coxeter groups whose dihedral angles are of the form π- m for m = 2,3,4,5,6, from: "Geometry and analysis of discrete groups and hyperbolic spaces" (editors M Fujii, N Kawazumi, K Ohshika), RIMS Kôkyûroku Bessatsu B66, RIMS (2017) 147 MR3821081
25 T Yukita, Growth rates of 3–dimensional hyperbolic Coxeter groups are Perron numbers, Canad. Math. Bull. 61 (2018) 405 MR3784769
26 T Yukita, On the continuity of the growth rate on the space of Coxeter systems, Groups Geom. Dyn. 18 (2024) 109