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Results tagged with field-with-one-element
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user 318
This tag refers to the (non-existent) "field of one element".
17
votes
Accepted
K(F_1) = sphere spectrum?
I understand that this is because GLn(F1) is supposed to be Sigman, the symmetric group on n letters. Thus K(F1) = K(finite sets) which is the sphere spectrum by the Barratt-Priddy-Quillen-Segal theor …
- 18.2k
13
votes
Accepted
Fundamental theorem of K-theory for loop groups over $\mathbb{F}_1$?
Let $G_n := W(\tilde{A}_{n-1})$. If I understand your description correctly, there is an extension
$$1 \to G_n \to S_{n} \wr \mathbb{Z} \overset{sum}\to \mathbb{Z} \to 1$$
and so a $\mathbb{Z}$-Galois …
- 18.2k