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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 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 …

Sanath, you will be happy to learn that I do have these notes. I'll give them to you to copy after you arrive in Chicago Monday.

Working simplicially (in those days called "semi-simplicially") this is surely due to Moore, with details in unpublished 1956 lecture notes and in John C. Moore, Semi-simplicial complexes and Postniko …

I suppose I should try to answer since the question of whether or not $BP$ is an $E_{\infty}$ ring spectrum was Problem 1 of "Problems in infinite loop space theory'', http://www.math.uchicago.edu/~ma …

There are several different, provably equivalent, definitions. Construction 10 in http://www.math.uchicago.edu/~may/PAPERS/23.pdf is one example. It is used to prove the uniqueness of a machine takin …

The late Gaunce Lewis's 1978 PhD thesis ``The stable category and generalized Thom spectra'' proved (as a special case) that the Thom spectra of $F$ and its oriented version $SF$ (alias $GL_1(S)$ or $ …

Since Denis gave the right reference, namely http://www.math.uchicago.edu/~may/BOOKS/equi.pdf, I did not follow up and answer this question. We can work with any compact Lie group and any complete un …

A. The brackets are the same computed in any model, as you say, and for most that entails fibrant approximation. For genuine $G$-spectra (complete universe), $G$ a compact Lie group, it goes back …

There is a comprehensive set of calculations of the homology of classical groups over finite fields in Z. Fiedorowicz and S. Priddy. Homology of classical groups over finite fields and their associate …

This is not quite what you mean, but relevant. Remember that a strictly associative and unital symmetric monoidal category is called a permutative category. I observed ages ago (http://www.math.uchi …

There is a very careful analysis of this question in Lemma 3.4.2, page 57, of More Concise Algebraic Topology, by Kate Ponto and myself. Assuming that $E$ and $B$ are connected, a fibration $E\longrig …

my friend, I have an email! But I can offer the history. First, although the $E_{\infty}$ book was published in 1977, it is a shotgun marriage of a bunch of earlier preprints that were rejected for …

Using the language of the two-sided bar construction, one can see the classifying map as follows. There is an evident natural zigzag of maps of principal $G$-bundles $$ P \longleftarrow B(P,G,G) \l …

That was a large part of the subject of my 1964 PhD thesis. While the motivation came from algebraic topology, the relevant algebra was published separately in the paper http://www.math.uchicago.edu …