Diameters of 3-Sphere Quotients
| dc.creator | Dunbar, W. | |
| dc.creator | Greenwald, S. | |
| dc.creator | McGowan, J. | |
| dc.creator | Searle, C. | |
| dc.date | 2007-02-23 | |
| dc.date.accessioned | 2026-07-07T07:48:29Z | |
| dc.date.available | 2026-07-07T07:48:29Z | |
| dc.description | Let G, a subset of O(4), act isometrically on the 3-sphere. In this article we calculate a lower bound for the diameter of the quotient spaces $S^3/G$. We find it to be ${1/2}\arccos(\frac{\tan(\frac{3 π}{10})}{\sqrt3})$, which is exactly the value of the lower bound for diameters of the spherical space forms. In the process, we are also able to find a lower bound for diameters for the spherical Aleksandrov spaces, $S^n/G$, of cohomogeneities 1 and 2, as well as for cohomogeneity 3 (with some restrictions on the group type). This leads us to conjecture that the diameter of $S^n/G$ is increasing as the cohomogeneity of the group $G$ increases. | |
| dc.description | The figure on page 12 previews and prints reliably with Adobe Reader | |
| dc.identifier | https://arxiv.org/abs/math/0702680 | |
| dc.identifier | http://arxiv.org/abs/math/0702680 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124515 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C20 | |
| dc.title | Diameters of 3-Sphere Quotients | |
| dc.type | text |