7,699 research outputs found
Thick hyperbolic 3-manifolds with bounded rank
We construct a geometric decomposition for the convex core of a thick
hyperbolic 3-manifold M with bounded rank. Corollaries include upper bounds in
terms of rank and injectivity radius on the Heegaard genus of M and on the
radius of any embedded ball in the convex core of M.Comment: 170 pages, 17 figure
Extending pseudo-Anosov maps to compression bodies
We show that a pseudo-Anosov map on a boundary component of an irreducible
3-manifold has a power that partially extends to the interior if and only if
its (un)stable lamination is a projective limit of meridians. The proof is
through 3-dimensional hyperbolic geometry, and involves an investigation of
algebraic limits of convex cocompact compression bodies.Comment: 29 page
Realising end invariants by limits of minimally parabolic, geometrically finite groups
We shall show that for a given homeomorphism type and a set of end invariants
(including the parabolic locus) with necessary topological conditions which a
topologically tame Kleinian group with that homeomorphism type must satisfy,
there is an algebraic limit of minimally parabolic, geometrically finite
Kleinian groups which has exactly that homeomorphism type and end invariants.
This shows that the Bers-Sullivan-Thurston density conjecture follows from
Marden's conjecture proved by Agol, Calegari-Gabai combined with Thurston's
uniformisation theorem and the ending lamination conjecture proved by Minsky,
partially collaborating with Masur, Brock and Canary.Comment: fourth version: Introduction rewritten; some arguments in Sec. 5 and
6 clarified
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