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Okay, so I'm pretty sure I have a sort-of answer for this for $f=x+y+\sum_{i,j>0}a_{ij}x^iy^j$, though it's not a closed form at all. With a bit of fiddling one can see that $$ f\circ f = \sum_{i,j> …

Perhaps this question is too elementary, but if it's written down anywhere, I'd love to know about it. Suppose I have a power series $f\in R[[x,y]]$ for some commutative, unital ring. I've recently be …

Faithfully flat Hopf-Galois extensions of rings: $A\to B$, with $H$ coacting on $B$ such that $B\otimes_AB\simeq B\otimes H$, are often thought of as being accessible substitutes for $G$-torsors in th …

This is essentially a reference request, or a request for an explanation of why this cannot be done in a useful or interesting way (i.e. an explanation of why no such reference exists!). If I have a d …

Is there a classification of the compact MU or BP modules in any category of spectra? Can the periodicity theorem be finagled to give a MU-module structure on finite spectra?

Does anyone know of a good, complete reference for non-commutative formal group laws (i.e. construction of a "Lazard ring," discussion of non-commutative formal groups, perhaps some discussion of thei …

In their book, Elmendorf, Kriz, May and Mandell describe a useful category of spectra, called S-modules, where S is the sphere spectrum. Ring objects in this category can be identified with spectra wi …

Suppose I have a spectrum $X$ and two homology theories $E$ and $F$. If I look at the Bousfield localizations, $L_E$, $L_F$, $L_{E\vee F}$ and $L_{E\wedge F}$, do I have a homotopy pullback square wh …

I have been informed that there is a reference out there which specifically details what goes wrong with the mod 2 Moore spectrum, i.e. why it is not $A_\infty$ or something? I do not know the details …

It is an old theorem of Heaton's (based on work of Eilenberg and MacLane), that a polynomial 3-cocycle $f(x,y,z)$ which is "symmetric," in the sense that $f(x,y,z)-f(x,z,y)+f(z,x,y)=0$, is always a co …

In May and Sigurdsson's Parameterized Homotopy Theory, Proposition 2.2.11, four isomorphisms of functors are given. For a pullback square of base spaces $C=holim(A\overset{f}\to B\overset{j}\leftarrow …

Given a monoidal model category $(M,\otimes, 1)$, and a monoid therein $A$, one can take the slice model category $M_{/A}$. This category has a natural monoidal structure induced by taking fibered pro …

Does anyone have a good reference for the method of giving a topology to a distributive lattice as outlined in M.H. Stone's "Topological representation of distributive lattices and Brouwerian logics"? …

This is primarily a reference request. Does anyone know of any writing about algebraic K-theory spectra picking up elements in the stable homotopy groups of spheres in their Hurewicz image coming from …

I'm essentially trying to figure out exactly what the title asks for. I've been scouring old Seminaires Henri Cartan and books by Stong to try to see exactly how to do this, but the combination of Fre …