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Tameness on the boundary and Ahlfors' measure conjecture

Jeffrey Brock, Kenneth Bromberg, Richard Evans, Juan Souto (2003)

Publications Mathématiques de l'IHÉS

Let N be a complete hyperbolic 3-manifold that is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We show N is homeomorphic to the interior of a compact 3-manifold, or tame, if one of the following conditions holds: 1. N has non-empty conformal boundary, 2. N is not homotopy equivalent to a compression body, or 3. N is a strong limit of geometrically finite manifolds. The first case proves Ahlfors’ measure conjecture for kleinian groups in the closure of the geometrically finite...

Taut foliations of 3-manifolds and suspensions of S 1

David Gabai (1992)

Annales de l'institut Fourier

Let M be a compact oriented 3-manifold whose boundary contains a single torus P and let ℱ be a taut foliation on M whose restriction to ∂ M has a Reeb component. The main technical result of the paper, asserts that if N is obtained by Dehn filling P along any curve not parallel to the Reeb component, then N has a taut foliation.

The cohomology algebras of orientable Seifert manifolds and applications to Lusternik-Schnirelmann category

J. Bryden, P. Zvengrowski (1998)

Banach Center Publications

This note gives a complete description of the cohomology algebra of any orientable Seifert manifold with ℤ/p coefficients, for an arbitrary prime p. As an application, the existence of a degree one map from an orientable Seifert manifold onto a lens space is completely determined. A second application shows that the Lusternik-Schnirelmann category for a large class of Seifert manifolds is equal to 3, which in turn is used to verify the Ganea conjecture for these Seifert manifolds.

The end curve theorem for normal complex surface singularities

Walter D. Neumann, Jonathan Wahl (2010)

Journal of the European Mathematical Society

We prove the “End Curve Theorem,” which states that a normal surface singularity ( X , o ) with rational homology sphere link Σ is a splice quotient singularity if and only if it has an end curve function for each leaf of a good resolution tree. An “end curve function” is an analytic function ( X , o ) → ( ℂ , 0 ) whose zero set intersects Σ in the knot given by a meridian curve of the exceptional curve corresponding to the given leaf. A “splice quotient singularity” ( X , o ) is described by giving an explicit set of equations describing...

The Fukumoto-Furuta and the Ozsváth-Szabó invariants for spherical 3-manifolds

Masaaki Ue (2009)

Banach Center Publications

We show that the Fukumoto-Furuta invariant for a rational homology 3-sphere M, which coincides with the Neumann-Siebenmann invariant for a Seifert rational homology 3-sphere, is the same as the Ozsváth-Szabó's correction term derived from the Heegaard Floer homology theory if M is a spherical 3-manifold.

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