Three-dimensional connected groups of automorphisms of toroidal circle planes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866911518939938816 |
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| author | Creutz, Brendan Ho, Duy Steinke, Günter F. |
| author_facet | Creutz, Brendan Ho, Duy Steinke, Günter F. |
| contents | We contribute to the classification of toroidal circle planes and flat Minkowski planes possessing three-dimensional connected groups of automorphisms. When such a group is an almost simple Lie group, we show that it is isomorphic to $\text{PSL}(2,\mathbb{R})$. Using this result, we describe a framework for the full classification based on the action of the group on the point set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_03073 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Three-dimensional connected groups of automorphisms of toroidal circle planes Creutz, Brendan Ho, Duy Steinke, Günter F. Geometric Topology 51B15, 51H10 We contribute to the classification of toroidal circle planes and flat Minkowski planes possessing three-dimensional connected groups of automorphisms. When such a group is an almost simple Lie group, we show that it is isomorphic to $\text{PSL}(2,\mathbb{R})$. Using this result, we describe a framework for the full classification based on the action of the group on the point set. |
| title | Three-dimensional connected groups of automorphisms of toroidal circle planes |
| topic | Geometric Topology 51B15, 51H10 |
| url | https://arxiv.org/abs/1808.03073 |