Timeline for $\mathbb{A}^1$-homotopy classes of maps from and to $\mathbb{G}_m^n$
Current License: CC BY-SA 4.0
4 events
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| Mar 26, 2021 at 19:48 | comment | added | Arna | @Denis-CharlesCisinski, I too had in mind to think of [πΎπ,π] as a kind of loop space and pointed-maps version of $[πΎπ,π]_{\mathbb{A}^1}$ as a kind of fundamental group. Does that makes some sense? Using $\mathbb{G}_m^n$, or for that matter $\mathbb{P}^n$, as probe spaces to explore the topology of $S$ just as one does with spheres $S^n$ in classical homotopy theory seems like a fruitful idea. Would love your comments on it. | |
| Mar 22, 2021 at 9:04 | comment | added | D.-C. Cisinski | This is not an elementary question. It is easier if you replace the multiplicative group by the projective line. For instance, there is a nice and rather explicit motivic version of the degree, as in this paper of Cazanave: numdam.org/item/ASENS_2012_4_45_4_511_0 | |
| Mar 22, 2021 at 3:35 | review | First posts | |||
| Mar 22, 2021 at 7:00 | |||||
| Mar 22, 2021 at 3:35 | history | asked | Arna | CC BY-SA 4.0 |