Timeline for Is there an explicit Dold-Thom theorem?
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| Sep 14, 2018 at 0:27 | comment | added | Nicholas Kuhn | dvitek: the homotopy groups will stabilize when the homology groups do. Regarding your other question: imagine putting in suspensions of X into the X variable, or let X be a spectrum. The key case turns out to be spheres. | |
| Sep 13, 2018 at 17:53 | comment | added | dvitek | Maybe I'm missing something, but I'm not sure how helpful this is for my specific question about the homotopy groups of $\mathrm{Sym}^nX$. I agree that the paper of Dold you mention solves the problem for homology (and a later paper of Puppe, MR0216497, solves the problem for cohomology). Your comment about the factorization of the Hurewicz map seems far more useful: what do you mean by the "stable range" of that filtration? | |
| Sep 12, 2018 at 23:20 | history | edited | j.c. | CC BY-SA 4.0 |
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| Sep 12, 2018 at 20:13 | history | answered | Nicholas Kuhn | CC BY-SA 4.0 |