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Results tagged with hyperbolic-geometry
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user 6206
14
votes
Accepted
Which knots are singularities of a hyperbolic cone-manifold structures on $S^3$?
The results proved in
S. Kojima, "Deformations of hyperbolic 3-cone-manifolds",
J. Differential Geom. 49 (1998), no. 3, 469-516
provide complete answers to questions 1 and 3.
The main theorem of …
- 3,749
9
votes
The number of cusps of higher-dimensional hyperbolic manifolds
Dear all, today a paper by Kolpakov and Martelli on the arxiv appeared that shows that there exist lots of 4-dimensional cusped hyperbolic manifolds with one cusp. Here is the reference
http://arxiv. …
- 3,749
6
votes
center of fundamental group of finite volume-hyperbolic orbifold
Let $G$ be the fundamental group of your orbifold, and recall that $G$ is a lattice in the group of isometries of hyperbolic space.
An element in the center of $G$ has to fix every fixed point of any …
- 3,749
7
votes
Accepted
Is the cut locus of a generic point in a hyperbolic manifold a generic polyhedron?
The question you pose is stated as an open question (in the 3-dimensional hyperbolic case) in the following paper:
Díaz, Raquel; Ushijima, Akira
On the properness of some algebraic equations appearin …
- 3,749
10
votes
Do you know how to construct a compact hyperbolic 3-manifold with three or four totally geod...
A beautiful construction (relying on 2-dimensional hyperbolic circle packings) of hyperbolic 3-manifolds with many totally geodesic boundary components can be found in the paper
Totally geodesic bound …
- 3,749