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| bio | website | |
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| location | ||
| age | ||
| visits | member for | 2 months |
| seen | 14 hours ago | |
| stats | profile views | 9 |
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May 16 |
comment |
Functoriality of the Fundamental group @Dan. Sure - that was a poorly worded comment. For example something like $BS^3$ is probably not an E-M space |
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May 16 |
comment |
Why base point makes a huge difference? It's a Dover book, and you can get it for around $10 (or an equivalent in your local currency!) |
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May 16 |
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filtration on the (co)homology of a space from the filtration of a space I wouldn't look at the Serre spectral sequence part. I'd just look up the section on the spectral sequence associated to a filtered complex. |
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May 16 |
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Functoriality of the Fundamental group What if we take, for example, $G=S^1$?. Then $BG = K(\mathbb{Z},2)$. $BG$ is not always an E-M space |
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May 15 |
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What is $\pi_{31}(S^2)$? I think the 64 refers to Kochman's work, but he was working stably. The tables of Toda only go out to 19. |
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May 15 |
awarded | Commentator |
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May 15 |
comment |
Why base point makes a huge difference? Oh OK! You can also find a nice proof in Mosher & Tangora's book (if you can find a copy) |
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May 15 |
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Why base point makes a huge difference? I'm not sure why you don't feel comfortable. Principal $S^1$ bundles are in correspondence with maps $[X,\mathbb{C} P^\infty] = [X,K(\mathbb{Z},2)]$. Since the Eilenberg-Maclane spaces represent homology this is just $H^2(X;\mathbb{Z}) = \mathbb{Z}$ for a surface. |
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May 14 |
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Why base point makes a huge difference? @user32240: $\mathbb{R}/\mathbb{Z} = S^1$ |
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May 14 |
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Why base point makes a huge difference? When you write $[Z,Y]$ be you mean based on unbased homotopy classes of maps? |
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May 14 |
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Why base point makes a huge difference? I think you have your example backwards. $B\mathbb{Z} = S^1$. $BS^1 = \mathbb{C}P^\infty$ |
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May 14 |
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Tor and flat base change Thanks Tyler. I agree with what you are saying. (I emailed Rotman and it appears it is just an error in the book) |
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May 12 |
awarded | Teacher |
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May 12 |
answered | Spectral sequences: equivalence of exact couples and classic (?) method |
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Mar 6 |
awarded | Scholar |
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Mar 6 |
awarded | Supporter |
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Mar 6 |
accepted | Tor and flat base change |
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Feb 28 |
comment |
Tor and flat base change Right. Which is exactly what Rotman (seems to be) assuming |
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Feb 28 |
awarded | Editor |
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Feb 28 |
comment |
Tor and flat base change Thanks. I've always thought this was the case. The proof he gives is definitely only on one side. I've sketched it above, along with the part that I don't quite see. |
