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Apr 24, 2013 at 21:39 vote accept Peter Crooks
Apr 24, 2013 at 21:19 comment added Ronnie Brown @Liviu: You have the get out word "elementary"! My problem with exact and spectral sequences has long been determining the possible extensions, since that was what my thesis was about, for function spaces. So I was quite surprised later to get with a groupoid van Kampen theorem precise colimit results involving consecutive dimensions. Analysing the reasons of this success was one of the intuitions behind the book referred to in my answer, namely the intuition of requiring invariants with structure in a range of dimensions, groupoids having structure in dimensions $0$ and $1$. So, ...
Apr 24, 2013 at 14:56 history answered Liviu Nicolaescu CC BY-SA 3.0