Timeline for Which topological spaces are (topological) groups?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Feb 23, 2013 at 15:48 | comment | added | Ralph | @mkreisel: $S^n$ for $n\neq 1,3,7$ odd are counter-examples. For, $H^\ast(S^n)=\mathbb{Q}[X]/(X^n),$ $\deg x=n$ is exterior, but only $S^1,S^3,S^7$ admit a H-space structure (Hatcher, 3.C). | |
| Feb 23, 2013 at 14:51 | comment | added | mkreisel | Is this condition sufficient? Are there "fake groups" or "fake H-spaces" with the right structure on cohomology but no actual group structure? | |
| Feb 23, 2013 at 12:17 | comment | added | Tom Goodwillie | Along the same lines, the fundamental group must be abelian. Note that these are restrictions on the (weak) homotopy type of the space. | |
| Feb 23, 2013 at 11:43 | history | answered | Ralph | CC BY-SA 3.0 |