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Questions designed to get an overview of a specific subject or body of results or to understand the relations among similar definitions, techniques or concepts appearing in different sub-fields of mathematics. While such questions by their very nature sometimes cannot be made very narrow and focused, it can be helpful to keep in mind that the design of MathOverflow does not make it a good fit for questions that are too broad.
9
votes
how do you visualize characteristic class?
This is a variation on standard answers (to this standard question). I'll start with a bit of philosophy since you mentioned different ways to think of cohomology. Singular cohomology is fairly "tra …
4
votes
Natural setting for characteristic classes?
[I tried to make this a comment, but ran out of space...]
I'm not 100% clear on your question, but do see some possible answer(s).
The homotopical generalization of a manifold is a Poincare duality …