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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 …
Roberto Frigerio's user avatar
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. …
Roberto Frigerio's user avatar
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 …
Roberto Frigerio's user avatar
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 …
Roberto Frigerio's user avatar
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 …
Roberto Frigerio's user avatar