The Geometry of Finitely Generated Kleinian Groups

We summarize properties of 3-manifold groups, with a particular focus on the consequences of the recent results of Ian Agol, Jeremy Kahn, Vladimir Markovic and Dani Wise.

3-Manifold Groups

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.

/pdf/shrinkwrapping-and-the-taming-of-hyperbolic-3-manifolds-2e13ljbr7n.pdf

Shrinkwrapping and the taming of hyperbolic 3-manifolds

Sous groupe de PSl(2,C). Familles holomorphes d'homeomorphismes de C•λ-lemme. Champs de ligne invariants. Familles holomorphes de groupes abstraitement isomorphes, car finiment genere. La stabilite structurelle implique geometriquement fini ou rigide. Theoreme A avec paraboles. Stabilite structurelle au sens de la dynamique differentiable

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Quasiconformal homeomorphisms and dynamics II: Structural stability implies hyperbolicity for Kleinian groups

A covering theorem for hyperbolic 3-manifolds and its applications

Compact Submanifolds of 3-Manifolds

Finitely Generated 3-Manifold Groups are Finitely Presented

This thesis consists of four papers, entitled

(i) Homotopy links,
(ii) A Note on Piecewise-linear Immersions,
(iii) Open and Closed Disc Bundles,
(iv) The Space of Homeomorphisms of a 2-manifold.

In (i), we define homotopy links and caloulate them in the metastable range.

In (ii), we prove the Haefliger-Poenaru immersion theorem, using block bundles.

In (iii), we prove that 02 = PL2(I) = PL2.

In (iv), we prove that the space of PL homeomorphisms of a 2-manifold, fixed on the boundary and an interior point, has contractible identity component unless the manifold is S2 or P2.

G. P. Scott

Papers

Compact Submanifolds of 3-Manifolds

Finitely Generated 3-Manifold Groups are Finitely Presented

Some problems in topology