| 论坛嘉宾: 萍踪浪迹 gauge 季候风 |
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kanex  发表文章数: 447
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不知哪里可以找到H^m(K(G,n))的资料。譬如，G=Z_p时。
 Récoltes et semailles
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季候风  发表文章数: 262
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classifying space 只是 K(G,1) 吧. 这个空间的上同调就是 G 的上同调, 可以直接用定义计算.
至于一般的 Eilenberg-Mclane space K(G,n) 我就不知道了.
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kanex 发表文章数: 447
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Obviously, I mean the general case....
Récoltes et semailles
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leo2000 发表文章数: 24
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For K(Z_p,1), I think you can figure it out yourself. Consider the
Z_p action on S^{\infty}, it is similar to RP^{\infty} which is K(Z_2,1). When n>1, using Leray spectral sequence, we can get H^i(K(Z_p; n);Q)= Q when i=0 =0 otherwise.
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kanex 发表文章数: 447
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Yes, these things are calculated by spectral sequences. But if you tensor the theory with Q, then the result is too simple. It's the torsion part which is the most mysterious and which have number theory implications.
Récoltes et semailles
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leo2000 发表文章数: 24
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I think you can use spectral sequence to compute some easy examples with
Z-coefficient. But in general, I don't know if they are all computable. I believe you need some very special technique in the manipulation of spectral sequence when you do the calculations. (for example: Steerod operations and some vanishing theorems ).
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kanex 发表文章数: 447
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I remember that I saw on Hatcher's AT book that it's computable and computed by someone. I wonder if there is a table of this, and any interesting things happening here.
p.s. check this if you haven't. http://math.ucr.edu/home/baez/counting/ The cohomology of classifying space / the higher homotopy of sphere may have some direct number theory implications. Récoltes et semailles
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leo2000 发表文章数: 24
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hope you can find what A.Hatcher says in his algebraic topology book.
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Cohomology of classifying space 
Re: Cohomology of classifying space 
Re: Cohomology of classifying space 
Re: Cohomology of classifying space