Timeline for Finite subgroup of $\mathrm{SO}(4)$ which acts freely on $\mathbb{S}^3$
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| S Nov 15, 2021 at 11:04 | history | bounty ended | CommunityBot | ||
| S Nov 15, 2021 at 11:04 | history | notice removed | CommunityBot | ||
| Nov 15, 2021 at 9:52 | comment | added | M. Winter | When I think about how groups act on spaces I usually think of an object which has this group as group of symmetry. Therefore your question reminded me of this answer in which Günter Rote describes a 4-polytope whose orientation-preserving symmetry group is $I\times C_7$ (one of the central extension of the icosahedral group mentioned on the Wikiepdia page). Since each of your groups $\Gamma$ is (abstractly) such a central extensions of a polyhedral group, an analogous construction should give you an object with symmetry group $\Gamma$. | |
| S Nov 7, 2021 at 9:55 | history | bounty started | Adterram | ||
| S Nov 7, 2021 at 9:55 | history | notice added | Adterram | Canonical answer required | |
| Nov 5, 2021 at 16:14 | comment | added | Ryan Budney | This is in Thurston's textbook, in the spherical 3-manifolds chapter. The precise embedding in $O_4$ is given. | |
| Nov 5, 2021 at 15:59 | comment | added | user43326 | @NickL Thank you very much, it helps already, but they only say which group "can" act, but they don't say how these groups "do" act, or, in other words, how they are included in SO(3), or did I miss something? | |
| Nov 5, 2021 at 10:39 | comment | added | Nick L | @user43326, here it is en.wikipedia.org/wiki/Spherical_3-manifold | |
| Nov 5, 2021 at 10:06 | comment | added | user43326 | I think it helps if you give us the classification of $\Gamma $. | |
| Nov 5, 2021 at 10:05 | history | edited | user43326 |
Added the at tag
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| Nov 5, 2021 at 7:26 | history | edited | YCor | CC BY-SA 4.0 |
formatting, added tag
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| Nov 5, 2021 at 7:17 | history | asked | Adterram | CC BY-SA 4.0 |