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arXiv · 1201.6104

Blowing up and down compacta with geometrically finite convergence actions of a group

Yoshifumi Matsuda·Shin-ichi Oguni·Saeko Yamagata
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Abstract

We consider two compacta with minimal non-elementary convergence actions of a countable group. When there exists an equivariant continuous map from one to the other, we call the first a blow-up of the second and the second a blow-down of the first. When both actions are geometrically finite, it is shown that one is a blow-up of the other if and only if each parabolic subgroup with respect to the first is parabolic with respect to the second. As an application, for each compactum with a geometrically finite convergence action, we construct its blow-downs with convergence actions which are not geometrically finite.

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Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata. 2013-05-31. Blowing up and down compacta with geometrically finite convergence actions of a group. https://arxiv.org/abs/1201.6104

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