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Results tagged with hyperbolic-geometry
Search options answers only
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user 9062
9
votes
Accepted
invariant 2-form in hyperbolic 3-space
In upper half space, the thing that's analogous to the invariant 2-form (which measures hyperbolic area) is the hyperbolic volume form $1/z^3 dx dy dz$.
If you want to understand 2-forms invariant by …
- 25.1k
19
votes
Accepted
Is there an explicit bound on the number of tetrahedra needed to triangulate a hyperbolic 3-...
A couple of things are true:
1. If you have any Riemannian manifold of bounded infinitesimal geometry (curvature pinched above and below), its thick part, where the injectivity radius $> \epsilon$, c …
- 25.1k
6
votes
Accepted
Fundamental group of a thick part of hyperbolic manifold
Yes, because $\pi_1$ of the boundary of a component of the $\epsilon$-thin part always
surjects to the fundamental group of that thin part, except in one special 2-dimensional
case: if there is a shor …
- 25.1k
20
votes
Accepted
Detecting a cover of the figure-8 knot complement
Edited, in light of description of manifold in comments (at end)
Added #2: The answer is no, details at the end
In principle this is doable, but caution is necessary. Given a manifold tiled by
ideal …
- 25.1k