Search Results

I think it might be pretty hard to get an answer that says nothing about cohomology. I interpret/think of Brown Representability as saying that if you want to think about these types of invariants you …

In "An alegbraic approach to the Steenrod algebra" Peter May writes down pretty much all the situations where you could have the action of Steenrod "like" operations. The most relevant case here is th …

When doing things related to free resolutions you may want the actual computation or you may want something highly structured. For the former you use the koszul resolution, it is nice and little and s …

The adams spectral sequence certainly does compute the desired result. But it sounds like you are looking for something to do/understand. by homogeneous spaces do you mean G/H for two lie groups? in t …

All the above answers are great, but as you are just learning this stuff, the following might be helpful. Vector/$G$-bundles contain actual geometric information! The tangent bundle, for example, tell …

There is the paper of R. V. Mikhailov and J. Wu, http://arxiv.org/abs/1108.3055. They construct a group whose center is an unstable homotopy group of either a sphere or a Moore space. So now it seems …

The reason may be slightly historical, the first examples of spectra were most easily seen to be indexed over the natural numbers: $MU$, $HR$, and $\mathbb{S}$. Now though, we know we ought to be usin …

This is not the duality that was asked for in the question, but it does show a way in which the Steenrod algebra structure is related to the Dyer-Lashof algebra structure. The Dyer-Lashof algebra can …

What about the following short note? https://neil-strickland.staff.shef.ac.uk/courses/bestiary/ss.pdf

It is definitely not an easy read, but you might want to have a look at Peter May's Classifying Spaces and Fibrations monograph. If i recall correctly, he constructs classifying spaces for fibrations …

Maybe this isn't the "right" way to think about them, but I have often found the following characterization much more appealing: the characteristic classes are just elements of $E^*(BG)$ for some coho …

decided to leave this as an answer instead of a comment: May wrote a book called classifying spaces and fibrations where he constructs such classifying spaces (you can get a copy of it for free on his …

You might want to take a look at Milnor and Stasheff. In section 9, oriented bundles and the euler class, they prove that if a bundle has a nowhere zero section then the euler class of that bundle is …

There was a fundamental error in my answer. The error was in misunderstanding the naturality of the $w_i$. $f: L \to N$ inducing an isomorphism in cohomology does not imply anything about the induced …

I would look at Stefan Schwede's articles. I think the answer is yes, see page 7 of Schwede and Shipley: http://www.math.uni-bonn.de/people/schwede/AlgebrasModules.pdf Perhpas this more explicitly st …