Scissors Congruence, the Golden Ratio and Volumes in Hyperbolic 5-Space
نویسنده
چکیده
By different scissors congruence techniques a number of dissection identities are presented between certain quasi-Coxeter polytopes, whose parameters are related to the golden section, and an ideal regular simplex in hyperbolic 5-space. As a consequence, several hyperbolic polyhedral 5-volumes can be computed explicitly in terms of Apéry’s constant ζ(3) and the trilogarithmic valueL3(π5 ).
منابع مشابه
Hilbert’s 3rd Problem and Invariants of 3–manifolds
This paper is an expansion of my lecture for David Epstein’s birthday, which traced a logical progression from ideas of Euclid on subdividing polygons to some recent research on invariants of hyperbolic 3– manifolds. This “logical progression” makes a good story but distorts history a bit: the ultimate aims of the characters in the story were often far from 3–manifold theory. We start in sectio...
متن کاملA Smooth Scissors Congruence Problem
Classifying space techniques are used to solve a smooth version of the classical scissors congruence problem.
متن کاملIntegral Congruence Two Hyperbolic 5-manifolds
Abstract. In this paper, we classify all the orientable hyperbolic 5-manifolds that arise as a hyperbolic space form H/Γ where Γ is a torsion-free subgroup of minimal index of the congruence two subgroup Γ 2 of the group Γ of positive units of the Lorentzian quadratic form x 1 + · · ·+ x 5 − x 6 . We also show that Γ 2 is a reflection group with respect to a 5-dimensional right-angled convex po...
متن کاملBloch Invariants of Hyperbolic 3-manifolds
We define an invariant β(M) of a finite volume hyperbolic 3manifoldM in the Bloch group B(C) and show it is determined by the simplex parameters of any degree one ideal triangulation of M . We show β(M) lies in a subgroup of B(C) of finite Q-rank determined by the invariant trace field of M . Moreover, the Chern-Simons invariant of M is determined modulo rationals by β(M). This leads to a simpl...
متن کاملBloch Invariants of Hyperbolic 3 - Manifoldswalter
We deene an invariant (M) of a nite volume hyperbolic 3-manifold M in the Bloch group B(C) and show it is determined by the simplex parameters of any degree one ideal triangulation of M. We show (M) lies in a subgroup of B(C) of nite Q-rank determined by the invariant trace eld of M. Moreover, the Chern-Simons invariant of M is determined modulo ra-tionals by (M). This leads to a simplicial for...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete & Computational Geometry
دوره 47 شماره
صفحات -
تاریخ انتشار 2012