## New answers tagged hyperbolic-geometry

1
vote

### Canonically representing the monodromy of a hyperbolic manifold fibered over $S^1$

The pseudo-Anosov homeomorphism is a diffeomorphism away from finitely many points, so in general will not be a smooth diffeomorphism. However, for certain fibered knots there are not singularities ...

- 63.6k

3
votes

### Canonically representing the monodromy of a hyperbolic manifold fibered over $S^1$

Here is an answer of sorts; it is not completely canonical though. First of all, you have to pick a conformal or hyperbolic structure on the fiber $\Sigma$. This can be made almost canonical, since ...

- 8,244

2
votes

Accepted

### Inheritance of arithmeticity properties in orbifold strata

Here is what I think is the correct setup:
Let $X$ be a symmetric space of noncompact type, $\Gamma$ is a lattice in the isometry group of $X$. Then $\Gamma$ has finitely many $\Gamma$-conjugacy ...

- 8,244

2
votes

### A question from the paper "Hyperbolic rigidity of higher rank lattices" by Thomas Haettel

Haettel is correct that the statement being used is part of the proof of the Tits alternative for HHGs.
There are more explicit references for the fact you mention.
The statement is that, if $H$ is a ...

- 312

0
votes

### $1$-Lipschitz map from hyperbolic to Euclidean plane

I have been informed that the result I was after is a special case of Lemma I.1.13 of "Metric spaces of non-positive curvature" by Bridson-Haefliger.

- 681

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