Minimum ideal triangulations of hyperbolic 3-manifolds
Colin Adams,W. Sherman +1 more
TLDR
It is shown that 2n−1 ≤σ(n)≤σor( n)≦4n−4 forn≥5 and that σor(n), the minimum number of ideal hyperbolic tetrahedra,≤2n for alln.Abstract:
Let ?(n) be the minimum number of ideal hyperbolic tetrahedra necessary to construct a finite volumen-cusped hyperbolic 3-manifold, orientable or not Let ?or(n) be the corresponding number when we restrict ourselves to orientable manifolds The correct values of ?(n) and ?or(n) and the corresponding manifolds are given forn=1,2,3,4 and 5 We then show that 2n?1≤?(n)≤?or(n)≤4n?4 forn?5 and that ?or(n)?2n for allnread more
Citations
More filters
Journal ArticleDOI
A census of cusped hyperbolic 3-manifolds
TL;DR: The census contains descriptions of all hyperbolic 3-manifolds obtained by gluing the faces of at most seven ideal tetrahedra and various geometric and topological invariants are calculated for these manifolds.
Journal ArticleDOI
Dehn Filling of the "Magic" 3-manifold
Bruno Martelli,Carlo Petronio +1 more
TL;DR: In this paper, the authors classified all non-hyperbolic Dehn fillings of the complement of the chain-link with 3 components, conjectured to be the smallest hyperbolic 3-manifold with 3 cusps.
Journal ArticleDOI
Symmetries of Hyperbolic 4-Manifolds
Alexander Kolpakov,Leone Slavich +1 more
TL;DR: In this paper, the first explicit examples of non-compact complete finite-volume arithmetic hyperbolic 4-manifolds M such that Isom M ∼ = G, or Isom + M ∼ ≥ G, were given.
Posted Content
The cusped hyperbolic census is complete
TL;DR: The SnapPea census as mentioned in this paper has been shown to be homeomorphic to one of the census manifolds, and has been extended to 9 tetrahedra, which is the first time it has been proven to be complete.
References
More filters
Journal ArticleDOI
Three dimensional manifolds, Kleinian groups and hyperbolic geometry
TL;DR: In the case of negative Euler characteristic (genus greater than 1) such a metric gives a hyperbolic structure: any small neighborhood in a surface is isometric to a neighborhood in the hyper-bolic plane, and the surface itself is the quotient of the hyperbola by a discrete group of motions as discussed by the authors.
Journal ArticleDOI
Rotation distance, triangulations, and hyperbolic geometry
Daniel D. Sleator,Daniel D. Sleator,Daniel D. Sleator,Robert E. Tarjan,William P. Thurston,William P. Thurston,William P. Thurston +6 more
TL;DR: In this paper, the authors established a tight bound of In 6 on the maximum rotation distance between two A2-node trees for all large n, using volumetric arguments in hyperbolic 3-space.
Journal ArticleDOI
Hyperbolic structures on 3-manifolds I: Deformation of acylindrical manifolds
TL;DR: In this article, the first in a series of papers showing that Haken manifolds have hyperbolic structures was published, the second two have existed only in preprint form, and later preprints were never completed.
Journal ArticleDOI
Euclidean decompositions of noncompact hyperbolic manifolds
David B. A. Epstein,R. C. Penner +1 more
TL;DR: In this paper, a methode for diviser a variete hyperbolique non compacte de volume fini en morceaux euclidiens canoniques is introduced.