Blowing up and down compacta with geometrically finite convergence actions of a group
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.
Keywords
Cite
@article{arxiv.1201.6104,
title = {Blowing up and down compacta with geometrically finite convergence actions of a group},
author = {Yoshifumi Matsuda and Shin-ichi Oguni and Saeko Yamagata},
journal= {arXiv preprint arXiv:1201.6104},
year = {2013}
}
Comments
26 pages, v2: Theorem 1.3 improved (see Theorems 1.4 and 1.5), Appendix B added, reference added, v3: organization of the paper modified, Remarks 1.3, 2.4 and 5.9 added, reference added