Timeline for Fundamental group of twisted loop space
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 27, 2021 at 14:49 | comment | added | Luigi M | no worries, I'm learning a lot from your question! thanks again | |
| Feb 27, 2021 at 14:48 | vote | accept | Luigi M | ||
| Feb 26, 2021 at 21:41 | comment | added | Mark Grant | You're welcome, I wish I had more time to think about this interesting question. In the simply connected case my 2nd exact sequence shows that $\pi_1(\Omega_f(M))$ is isomorphic to the cokernel of a map $\pi_2(M\times M)\to \pi_2(M\times M)$, which I believe should be given by $(x,y)\mapsto(x-y,f_*(x)-y)$. | |
| Feb 26, 2021 at 16:51 | comment | added | Luigi M | thanks a lot Mark. I'm wondering, is there a way to see from your second exact sequence that in the simply connected case, $\pi_1(\Omega_f(M))\cong \pi_2(M)$? | |
| Feb 26, 2021 at 15:07 | history | edited | Mark Grant | CC BY-SA 4.0 |
Major correction with different pullback and different conclusion.
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| Feb 26, 2021 at 14:55 | history | edited | Mark Grant | CC BY-SA 4.0 |
added 111 characters in body
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| Feb 26, 2021 at 14:29 | comment | added | Tyrone | In the homotopy pullback you suggest you have $\Omega_f(M)\simeq M$ and there isn't much interesting to say about $\pi_1$. I think you need a different construction to capture the problem. | |
| Feb 26, 2021 at 8:41 | history | answered | Mark Grant | CC BY-SA 4.0 |