Timeline for Reference request: Basic H-Space properties of $SO(3)$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 16, 2017 at 14:26 | comment | added | John R. Harper | Here are two papers with relevant information. Arkowitz,Ewing,Schiffman, Quart. J. Math. 26 (1975) 295-307; McGibbon,same journal 31 (1980) 341-350. One consequence is that the degree of an H-map from SO(3) to S^3 must be congruent to 0 or 8 mod 12. | |
| Sep 27, 2016 at 16:18 | comment | added | Tyrone | I'm not sure that an H-map need be a loop map. | |
| Sep 27, 2016 at 9:29 | comment | added | Lennart Meier | Regarding the first point: If we consider the composition $S^3 \to SO(3) \to S^3$, this has even degree. At least if the composite $f\colon S^3 \to S^3$ is a group homomorphism, it induces a map $Bf\colon \mathbb{HP}^\infty \to \mathbb{HP}^\infty$ of classifying spaces. If I understand it correctly, it must have odd degree when it is non-constant by Feder, S.; Gitler, S. Mappings of quaternionic projective spaces. This suggests that every $H$-map $SO(3) \to S^3$ might be constant. | |
| Sep 25, 2016 at 14:50 | history | edited | Tyrone | CC BY-SA 3.0 |
References and typo.
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| Sep 25, 2016 at 14:31 | history | asked | Tyrone | CC BY-SA 3.0 |