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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 abelianization of the Johnson kernel

Alexandru Dimca, Richard Hain, Stefan Papadima (2014)

Journal of the European Mathematical Society

We prove that the first complex homology of the Johnson subgroup of the Torelli group T g is a non-trivial, unipotent T g -module for all g ≥ 4 and give an explicit presentation of it as a S y m . H 1 ( T g , C ) -module when g ≥ 6 . We do this by proving that, for a finitely generated group G satisfying an assumption close to formality, the triviality of the restricted characteristic variety implies that the first homology of its Johnson kernel is a nilpotent module over the corresponding Laurent polynomial ring, isomorphic to the...

The ambient homeomorphy of certain function and sequence spaces

Jan J. Dijkstra, Jerzy Mogilski (1996)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider a number of sequence and function spaces that are known to be homeomorphic to the countable product of the linear space σ . The spaces we are interested in have a canonical imbedding in both a topological Hilbert space and a Hilbert cube. It turns out that when we consider these spaces as subsets of a Hilbert cube then there is only one topological type. For imbeddings in the countable product of lines there are two types depending on whether the space is contained in a...

The cell-like approximation theorem in dimension 5

Robert J. Daverman, Denise M. Halverson (2007)

Fundamenta Mathematicae

The cell-like approximation theorem of R. D. Edwards characterizes the n-manifolds precisely as the resolvable ENR homology n-manifolds with the disjoint disks property for 5 ≤ n < ∞. Since no proof for the n = 5 case has ever been published, we provide the missing details about the proof of the cell-like approximation theorem in dimension 5.

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