| 31. | A similar spectral sequence exists for group homology, as opposed to group cohomology, as well.
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| 32. | In the case studied by Lichtenbaum, the spectral sequence would degenerate, yielding Lichtenbaum's conjecture.
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| 33. | Putting the zero differential on all the rest of our sheets gives a spectral sequence whose terms are:
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| 34. | For example, this is true of the spectral sequence of a double complex, explained below .)
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| 35. | In most spectral sequences, the E _ \ infty term is not naturally a doubly graded object.
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| 36. | Using the spectral sequence of a filtered complex, we can derive the existence of long exact sequences.
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| 37. | More specifically, the " E " 2 term of this spectral sequence may be identified as
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| 38. | This is precisely the Atiyah-Hirzebruch spectral sequence construction of twisted K-theory as a set.
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| 39. | These filtrations are of particular interest because the Adams (-Novikov ) spectral sequence converges to them.
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| 40. | Unfortunately, because of the large amount of information carried in spectral sequences, they are difficult to grasp.
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