Timeline for What is $H^*(\mathbb{CP}^{2^N-1}/\Sigma_n;\mathbb{Z})$ when $N=\binom{n}{2}$?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 21, 2023 at 16:15 | history | edited | Jackson Walters | CC BY-SA 4.0 |
using math notation for cohomology
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| Sep 21, 2023 at 1:35 | comment | added | Jackson Walters | @QiaochuYuan Thank you, that’s clear. Thanks Jason as well. | |
| Sep 21, 2023 at 1:15 | comment | added | Jason Starr | What @QiaochuYuan said :) | |
| Sep 21, 2023 at 1:09 | comment | added | Qiaochu Yuan | This action comes from a linear action on $V^{\otimes N}$ and so it factors through the action of the general linear group $GL(V^{\otimes N})$, which is path-connected, so every element acts trivially on any homotopy invariant. | |
| Sep 20, 2023 at 23:55 | history | edited | Jackson Walters | CC BY-SA 4.0 |
remove obvious cohomology fact
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| Sep 20, 2023 at 23:50 | comment | added | Jackson Walters | @JasonStarr Okay, that answers that. Is it obvious why that's true? | |
| Sep 20, 2023 at 23:43 | comment | added | Jason Starr | The symmetric group acts trivially on the cohomology of $\mathbb{CP}^{2^N-1}$, as does the entire (projective linear group) of biholomorphisms of the projective space. So the entire cohomology ring is invariant. | |
| Sep 20, 2023 at 23:36 | history | edited | Jackson Walters | CC BY-SA 4.0 |
add \cdot
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| Sep 20, 2023 at 23:29 | history | edited | Jackson Walters | CC BY-SA 4.0 |
deleted 115 characters in body
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| Sep 20, 2023 at 23:23 | history | asked | Jackson Walters | CC BY-SA 4.0 |