Timeline for $\mathrm{String}/\mathbb{CP}^{\infty}=\mathrm{Spin}$ or a correction to this quotient group relation
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 7 at 14:15 | history | edited | LSpice | CC BY-SA 4.0 |
Title consistent with @DavidRoberts's edits
|
| Jun 7 at 0:55 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
formatting
|
| Jun 6 at 23:09 | history | edited | zeta | CC BY-SA 4.0 |
edited body
|
| May 19 at 9:13 | comment | added | Leo | Hi, I think your fiber sequence is wrong. It should be $B^3\mathbb{Z}\to B String(n)\to B Spin(n)\to B^4\mathbb{Z}$. The loop space appears to the left, not to the right. One good way to understand $String(n)$ is to view it as a smooth 2-group. | |
| Nov 24, 2023 at 13:37 | comment | added | Konrad Waldorf | There exists a model for the classifying space $BG$ of a topological group $G$, such that when $G$ is abelian, $BG$ is again an abelian group. This is Segal's construction, namely, the geometric realization of the groupoid with a single object with automorphism group $G$. The same is true for $EG$. | |
| Nov 24, 2023 at 13:16 | answer | added | Konrad Waldorf | timeline score: 5 | |
| Nov 24, 2023 at 8:57 | comment | added | Sebastian Goette | The projective unitary group $PU$ of a separable Hilbert space is weakly(?) homotopy equivalent to $\mathbb CP^\infty$. It is not abelian. | |
| Nov 23, 2023 at 18:55 | history | edited | Dmitri Pavlov | CC BY-SA 4.0 |
edited body
|
| Nov 23, 2023 at 18:52 | answer | added | Dmitri Pavlov | timeline score: 3 | |
| Nov 23, 2023 at 16:10 | history | asked | zeta | CC BY-SA 4.0 |