61 research outputs found
Shrinkwrapping and the taming of hyperbolic 3-manifolds
We introduce a new technique for finding CAT(-1) surfaces in hyperbolic
3-manifolds. We use this to show that a complete hyperbolic 3-manifold with
finitely generated fundamental group is geometrically and topologically tame.Comment: 60 pages, 7 figures; V3: incorporates referee's suggestions,
references update
Group negative curvature for 3-manifolds with genuine laminations
We show that if a closed atoroidal 3-manifold M contains a genuine
lamination, then it is group negatively curved in the sense of Gromov.
Specifically, we exploit the structure of the non-product complementary regions
of the genuine lamination and then apply the first author's Ubiquity Theorem to
show that M satisfies a linear isoperimetric inequality.Comment: 13 pages. Published copy, also available at
http://www.maths.warwick.ac.uk/gt/GTVol2/paper4.abs.htm
On the topology of ending lamination space
We show that if S is a finite type orientable surface of genus g and p
punctures where 3g+p > 4, then EL(S) is (n-1)-connected and (n-1)-locally
connected where dim(PML(S))=2n+1=6g+2p-7. Furthermore, if g=0, then EL(S) is
homeomorphic to the p-4 dimensional Nobeling space
Homotopy hyperbolic 3-manifolds are hyperbolic
This paper introduces a rigorous computer-assisted procedure for analyzing hyperbolic 3-manifolds. This procedure is used to complete the proof of several long-standing rigidity conjectures in 3-manifold theory as well as to provide a new lower bound for the volume of a closed orientable hyperbolic 3-manifold
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