Thickness of skeletons of arithmetic hyperbolic orbifolds
نویسندگان
چکیده
We show that closed arithmetic hyperbolic 3-dimensional orbifolds with larger and volumes give rise to triangulations of the underlying spaces whose 1-skeletons are harder embed nicely in Euclidean space. To this we generalize an inequality Gromov Guth n-orbifolds find nearly optimal geodesic 3-orbifolds.
منابع مشابه
Peripheral separability and cusps of arithmetic hyperbolic orbifolds
For X = R , C , or H , it is well known that cusp cross-sections of finite volume X –hyperbolic (n + 1)–orbifolds are flat n–orbifolds or almost flat orbifolds modelled on the (2n + 1)–dimensional Heisenberg group N2n+1 or the (4n + 3)–dimensional quaternionic Heisenberg group N4n+3(H). We give a necessary and sufficient condition for such manifolds to be diffeomorphic to a cusp cross-section o...
متن کاملCusps of Minimal Non-compact Arithmetic Hyperbolic 3-orbifolds
In this paper we count the number of cusps of minimal non-compact finite volume arithmetic hyperbolic 3-orbifolds. We show that for each N , the orbifolds of this kind which have exactly N cusps lie in a finite set of commensurability classes, but either an empty or an infinite number of isometry classes.
متن کاملCusps of arithmetic orbifolds
This thesis investigates cusp cross-sections of arithmetic real, complex, and quaternionic hyperbolic n–orbifolds. We give a smooth classification of these submanifolds and analyze their induced geometry. One of the primary tools is a new subgroup separability result for general arithmetic lattices. Cusps of arithmetic orbifolds 1
متن کاملEigenvalue Fields of Hyperbolic Orbifolds
In this paper, we prove that if Γ is a non-elementary subgroup of Oo(n, 1,R), with n ≥ 2, then the eigenvalue field of Γ has infinite degree over Q.
متن کاملHyperbolic Orbifolds of Minimal Volume
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 consequen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Topology and Analysis
سال: 2021
ISSN: ['1793-7167', '1793-5253']
DOI: https://doi.org/10.1142/s1793525321500321