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