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Oct 20, 2022 at 7:42 comment added Grisha Taroyan @NicholasKuhn No, I think here symmetric powers are considered in another sense. In particular, $K(\mathbb{Z},1)$ is a simplicial abelian group and we are taking symmetric powers of this object. Although, I am not completely sure how this works. I was also somewhat confused by this fact since the topological symmetric powers of a circle are indeed just a circle.
Oct 20, 2022 at 0:02 comment added Nicholas Kuhn Maybe I am misunderstanding your question about K(Z,1), but the symmetric products of the circle are all homotopy equivalent to a circle. Indeed there is an exercise in tom Dieck's book Transformation Groups that asks you to show that the nth symmetric product of the circle is a fibration over the circle with fiber an (n-1) simplex.
Oct 19, 2022 at 13:05 review Close votes
Oct 21, 2022 at 4:07
Oct 19, 2022 at 12:45 history edited Grisha Taroyan
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Oct 19, 2022 at 12:36 history asked Grisha Taroyan CC BY-SA 4.0