Displaying similar documents to “Pro- p groups and towers of rational homology spheres.”

Homology lens spaces and Dehn surgery on homology spheres

Craig Guilbault (1994)

Fundamenta Mathematicae

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A homology lens space is a closed 3-manifold with ℤ-homology groups isomorphic to those of a lens space. A useful theorem found in [Fu] states that a homology lens space M 3 may be obtained by an (n/1)-Dehn surgery on a homology 3-sphere if and only if the linking form of M 3 is equivalent to (1/n). In this note we generalize this result to cover all homology lens spaces, and in the process offer an alternative proof based on classical 3-manifold techniques.

The box-counting dimension for geometrically finite Kleinian groups

B. Stratmann, Mariusz Urbański (1996)

Fundamenta Mathematicae

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We calculate the box-counting dimension of the limit set of a general geometrically finite Kleinian group. Using the 'global measure formula' for the Patterson measure and using an estimate on the horoball counting function we show that the Hausdorff dimension of the limit set is equal to both: the box-counting dimension and packing dimension of the limit set. Thus, by a result of Sullivan, we conclude that for a geometrically finite group these three different types of dimension coincide...

Porosity of Collet–Eckmann Julia sets

Feliks Przytycki, Steffen Rohde (1998)

Fundamenta Mathematicae

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We prove that the Julia set of a rational map of the Riemann sphere satisfying the Collet-Eckmann condition and having no parabolic periodic point is mean porous, if it is not the whole sphere. It follows that the Minkowski dimension of the Julia set is less than 2.