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Is there an account in English of results from "Homologie nicht-additiver Funktoren. Anwendungen" by Dold and Puppe? I am mostly interested in the spectral sequence of cross-effects which computes the homology of a functor on the suspension (p.251) and in the fact that higher symmetric powers of $K(\mathbb{Z},1)$ are null-homotopic (p.306).

For context: I am trying to understand Curtis's paper "Lower central series of semi-simplicial complexes" and it relies on results by Dold and Puppe.

Of course, I am also interested in the modern approach to similar results if there is any.

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  • $\begingroup$ 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. $\endgroup$
    – Nicholas Kuhn
    Commented Oct 20, 2022 at 0:02
  • $\begingroup$ @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. $\endgroup$
    – Grisha Taroyan
    Commented Oct 20, 2022 at 7:42

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