Search Results

This is not an answer, but a little too long for a comment. Scott, what a list: 3 dead, 2 retired, and me; also I think Mike and I are always on the same side of the fence. As to the original questi …

A 2020 paper Operads, monoids, monads, and bar constructions by Ruozi Zhang, Foling Zou, and J.P. May revisits the foundations of operad theory and discusses several possible choices for what $\mathca …

I see no real point in considering $E_{\infty}$ spaces with $0$ except in the context of the multiplicative structure of an $E_{\infty}$ ring space or, essentially equivalently, the multiplicative str …

There are two old papers that address this topic in some detail: R. W. Thomason. Uniqueness of delooping machines. \url{https://projecteuclid.org/euclid.dmj/1077313403} Z. Fiedorowicz. Classifying …

There is so much much more. For one historical starting point among many, you see that many spaces of interest are infinite loop spaces and that tells you how to calculate things about them. For jus …

Notice the switch in grading from homology to cohomology on May's page 182: $P^s(x) = P_{-s}(x)$. Operations that raise degree when graded homologically lower degree when graded cohomologically. A la …

I'll take your question as license to advertise a relatively recent paper in a slightly more specialized but concretely calculational direction: http://nyjm.albany.edu/j/2014/20-53p.pdf. Its title …

I'm feeling mischievous. The history of the Kervaire invariant problem is strewn with false proofs, Jim Milgram's is only one of many. A student of mine (who I will leave nameless) had a preprint (a …

@FKranhold You mean I got it right? You had me fooled. I should apologize for leaving that detail to the reader, but let me give two excuses. First, one does not actually need that detail to prove L …

I have no idea what source you are quoting, but you are quite right that it is wrong, unless we are both screwing up. One builds $\phi_n$ rigorously by inducting on the stages of the construction of …

I would like to point out that the term "equivariant cohomology'' is ambiguous. To those unfamiliar with modern algebraic topology, it means Borel cohomology, the cohomology theory that is the subjec …

This is probably belaboring the obvious, but just take seriously the equivalence between grouplike $E_{\infty}$ spaces and connective spectra. See for example Equivalence between $E_\infty$-spaces …

I'm surprised this has been up for days with nobody telling Atticus the obvious. Let $I$ be the unit interval category with two objects, $0$ and $1$, and one non-identity arrow $0 \to 1$. A natural …

Yes it is true. You have correctly interpreted the intended meaning of the phrase ``fibration of infinite loop spaces''. One early reference is chapter I of $E_{\infty}$ ring spaces and $E_{\infty}$ …

Group completion and the answer to your questions (for $k\geq 2$) are probaby best understood homologically. An ancient definition is that a map $X\rightarrow Y$ of homotopy commutative $H$-spaces …