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Article
Tent property of the growth indicator functions and applications
Let \(\Gamma \) Γ be a Zariski dense discrete subgroup of a connected semis...
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Article
Fibered faces, veering triangulations, and the arc complex
We study the connections between subsurface projections in curve and arc complexes in fibered 3-manifolds and Agol’s veering triangulation. The main theme is that large-distance subsurfaces in fibers are assoc...
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Article
Thick-skinned 3-manifolds
We show that if the totally geodesic boundary of a compact hyperbolic 3-manifold M has a collar of depth \({d \gg 0}\) ...
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Article
Picture-Hanging Puzzles
We show how to hang a picture by wrap** rope around n nails, making a polynomial number of twists, such that the picture falls whenever any k out of the n nails get removed, and the picture remains hanging when...
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Article
On dynamics of Out(F n ) on PSL2(ℂ) characters
We introduce and study an open set of PSL2(ℂ) characters of a nonabelian free group, on which the action of the outer automorphism group is properly discontinuous, and which is strictly larger than the set of dis...
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Chapter and Conference Paper
Picture-Hanging Puzzles
We show how to hang a picture by wrap** rope around n nails, making a polynomial number of twists, such that the picture falls whenever any k out of the n nails get removed, and the picture remains hanging when...
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Article
Bounded geometry for Kleinian groups
We show that a Kleinian surface group, or hyperbolic 3-manifold with a cusp-preserving homotopy-equivalence to a surface, has bounded geometry if and only if there is an upper bound on an associated collection...
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Article
Geometry of the complex of curves I: Hyperbolicity
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Article
Spectral theory, Hausdorff dimension and the topology of hyperbolic 3-manifolds
Let M be a compact 3-manifold whose interior admits a complete hyperbolic structure. We let Λ(M) be the supremum of λ0(N) where N varies over all hyperbolic 3-manifolds homeomorphic to the interior of N. Similarl...