In: Discrete & Computational Geometry, 2012, vol. 47, no. 3, p. 629-658
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In: Tokyo Journal of Mathematics, 2017, vol. 40, no. 2, p. 379-391
In [7], Kellerhals and Perren conjectured that the growth rates of the reflection groups given by compact hyperbolic Coxeter polyhedra are always Perron numbers. We prove that this conjecture holds in the context of ideal Coxeter polyhedra in H3. Our methods allow us to bound from below the growth rates of composite ideal Coxeter polyhedra by the growth rates of its ideal Coxeter polyhedral...
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In: RIMS Kôkyûroku Bessatsu, 2017, vol. B66, p. 057-113
For hyperbolic Coxeter groups of finite covolume we review and present new theoretical and computational aspects of wide commensurability. We discuss separately the arithmetic and the non-arithmetic cases. Some worked examples are added as well as a panoramic viewto hyperbolic Coxeter groups and their classification.
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In: Mathematics, 2017, vol. 5, no. 3, p. 43
We study lattices with a non-compact fundamental domain of small volume in hyperbolic space H n . First, we identify the arithmetic lattices in Isom + H n of minimal covolume for even n up to 18. Then, we discuss the related problem in higher odd dimensions and provide solutions for n = 11 and n = 13 in terms of the rotation subgroup of certain Coxeter pyramid groups found by Tumarkin. The ...
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In: Geometriae Dedicata, 2016, vol. 183, no. 1, p. 143–167
For Coxeter groups acting non-cocompactly but with finite covolume on real hyperbolic space Hn, new methods are presented to distinguish them up to (wide) commensurability. We exploit these ideas and determine the commensurability classes of all hyperbolic Coxeter groups whose fundamental polyhedra are pyramids over a product of two simplices of positive dimensions.
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In: Computational Methods and Function Theory, 2014, p. 1–17
We provide a survey of hyperbolic orbifolds of minimal volume, starting with the results of Siegel in two dimensions and with the contributions of Gehring, Martin and others in three dimensions. For higher dimensions, we summarise some of the most important results, due to Belolipetsky, Emery and Hild, by discussing related features such as hyperbolic Coxeter groups, arithmeticity and...
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In: Algebraic & Geometric Topology
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In: Canadian Journal of Mathematics
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In: Algebraic & Geometric Topology
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In: Discrete & Computational Geometry, 2012, vol. 47, no. 3, p. 629-658
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