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