6/5/2023 0 Comments Spectral sequences![]() ![]() ![]() This spectral sequence is called the Adams spectral sequence and is a powerful tool for calculating the stable homotopy groups of spheres. ![]() For more information about this, see chapter 18 of Mosher and Tangora's Cohomology Operations. One can use a different filtration, called the Adams filtration, that is easy to describe in terms of known objects, but only yields the $2-$ primary part of $$. For more information about this spectral sequence see chapter 14 of Mosher and Tangora's Cohomology Operations an Applications to Homotopy Theory.īut one often doesn't know the information in the $E_2$ or $E_1$ group of this spectral sequence. Additional topics to be determined, depending on time remaining and interests of the class. One reasonably general example: The homology spectral sequence of a bunch of inclusions of toplogical spaces - Given a filtering of a topological space $0=X_)$. G evaluated at X X X is isomorphic to the Grothendieck spectral sequence of the composition of. The former will usually be known and the output is something that you wanted to know. Comparison of spectral sequences involving bifunctors. A spectral sequence is a tool to get from the homology of the associated graded of a filtered chain complex to the associate graded of the homology of the filtered chain complex. ![]()
0 Comments
Leave a Reply. |