| 41. | The spectral sequence need not degenerate, however, because the differential maps might not all be zero at once.
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| 42. | The skeletons of a space are used in obstruction theory, to construct spectral sequences by means of inductive arguments.
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| 43. | It is one of the fundamental stars of the MK spectral sequence, defined as type K1.5 Ib.
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| 44. | Spectral sequences are less essential in the derived category approach, but still play a role whenever concrete computations are necessary.
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| 45. | Moreover, etale " K "-theory admitted a spectral sequence similar to the one conjectured by Quillen.
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| 46. | The terms of this spectral sequence stabilize at the first sheet because its only nontrivial differential was on the zeroth sheet.
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| 47. | Determining differentials or finding ways to work around them is one of the main challenges to successfully applying a spectral sequence.
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| 48. | E _ \ infty ^ { p, q } is a natural candidate for the abutment of this spectral sequence.
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| 49. | Most modern computations use spectral sequences, a technique first applied to homotopy groups of spheres by Jean-Pierre Serre.
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| 50. | The spectral sequence for the group homology, together with the analysis of a differential in this spectral sequence, shows that
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