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4 | Rollback to Revision 2 | ||
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[Edit]: This is wrong!! See Peter's answer below. Unless I'm missing something, this follows from the naturality of the Serre spectral sequence. That is, each element of $g$ gives a map of fiber sequences, whence a map of Serre spectral sequences converging to the map on $H_*(E;\mathbb{Z})$. |
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3 | Removed "below" since Peter's answer is now "above"... | ||
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[Edit]: This is wrong!! See Peter's answerbelow. Unless I'm missing something, this follows from the naturality of the Serre spectral sequence. That is, each element of $g$ gives a map of fiber sequences, whence a map of Serre spectral sequences converging to the map on $H_*(E;\mathbb{Z})$. |
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2 | added 53 characters in body | ||
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[Edit]: This is wrong!! See Peter's answer below. Unless I'm missing something, this follows from the naturality of the Serre spectral sequence. That is, each element of $g$ gives a map of fiber sequences, whence a map of Serre spectral sequences converging to the map on $H_*(E;\mathbb{Z})$. |
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