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 Dec 4 awarded Nice Question Jun 3 comment Definitions of the ring $R/(x_0^\infty,\ldots,x_{n-1}^\infty)$ @Crostul: It's about half-way down. Is $R/(x_0^\infty,\ldots,x_{n-1}^\infty) \simeq R/I^\infty$? The rest is an attempt at a proof, but I'm not sure if it is correct! Jun 3 revised Definitions of the ring $R/(x_0^\infty,\ldots,x_{n-1}^\infty)$ consistency with $R$ and $A$ Jun 3 asked Definitions of the ring $R/(x_0^\infty,\ldots,x_{n-1}^\infty)$ May 22 awarded Enlightened May 22 awarded Nice Answer Feb 27 awarded Yearling Dec 13 awarded Caucus Oct 18 awarded Autobiographer Aug 18 answered homotopy class of maps in terms of homotopy groups of spectra Aug 18 comment homotopy class of maps in terms of homotopy groups of spectra This can't work for spaces since $[X,Y]$ is in general only a set. If you work with spectra instead of spaces (the very open) Freyd's generating hypothesis is that for finite spectra $X$ and $Y$ the natural map $[X,Y] \to \text{Hom}_{\pi_* S}(\pi_*X,\pi_* Y)$ is a monomorphism (which Freyd shows actually implies it is an isomorphism). Jul 22 answered Refining homotopy commutative maps of spectra to maps of E_{\infty}-ring spectra Mar 11 comment A group-like topological monoid is a loop space Opps, I have no idea how that happened. I think I meant to link to this: math.stanford.edu/~carym/bar.pdf Mar 11 comment A group-like topological monoid is a loop space This probably depends on your model for $BM$, but see, for example, math.stackexchange.com/questions/704397/… Feb 27 awarded Yearling Feb 19 comment A question about the universal coefficient theorem. I think if you're careful about it, you'll find that the maps can be chosen to be $R$-module maps, but that the splitting is not one of $R$-modules Jan 31 comment Universal Coefficient Theorem - what kind of morphisms? But here you know what the map $H_n(X) \otimes \mathbb{Q} \to H_n(X;\mathbb{Q})$ is - and you know (on the chain level) where the module structure is coming from Jan 30 comment Universal Coefficient Theorem - what kind of morphisms? The point is that $H_1(X;\mathbb{Q})\simeq H_1(X) \otimes \mathbb{Q}$ both as abelian groups and as a $\mathbb{Q}$-vector space Jan 30 comment Universal Coefficient Theorem - what kind of morphisms? As an example, what can you say about $H_1(X;\mathbb{Q})$ as an abelian group, and as a vector space? Jan 27 comment Cup Product Structure on the n-Torus See the bottom of pp. 242: math.cornell.edu/~hatcher/AT/ATcapprod.pdf