| 21. | The resulting Adams Novikov spectral sequence is now a basic tool in stable homotopy theory.
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| 22. | This is true even when many of the terms of the spectral sequence are incalculable.
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| 23. | The simplest situation in which we can determine convergence is when the spectral sequences degenerates.
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| 24. | Physicist typically want to calculate twisted K-theory using the Atiyah Hirzebruch spectral sequence.
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| 25. | Despite this, it is still possible to gain useful information from these two spectral sequences.
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| 26. | For example, consider the constraint on the Atiyah-Hirzebruch spectral sequence ( AHSS ):
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| 27. | The Tohoku paper also introduced the Grothendieck spectral sequence associated to the composition of derived functors.
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| 28. | Leray's work of this period proved seminal to the development of spectral sequences and sheaves.
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| 29. | While this can be verified without a spectral sequence, it is very easy with spectral sequences.
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| 30. | While this can be verified without a spectral sequence, it is very easy with spectral sequences.
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