Blowing up and down compacta with geometrically finite convergence actions of a group
Blowing up and down compacta with geometrically finite convergence actions of a group
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发表时间：
2012-01
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通讯作者：
Yoshifumi Matsuda;Shin-ichi Oguni;S. Yamagata
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作者：
Yoshifumi Matsuda;Shin-ichi Oguni;S. Yamagata
我们考虑两个具有可数群的最小非基本收敛动作的紧凑体。当存在从一个到另一个的等变连续映射时，我们将第一个称为第二个的放大，将第二个称为第一个的放大。当两个作用在几何上都是有限的时，表明当且仅当相对于第一个作用的每个抛物线子群相对于第二个作用是抛物线子群时，一个是另一个的放大。作为一个应用，对于每个具有几何有限收敛作用的密体，我们用非几何有限的收敛作用构造其放空。
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.