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Adams Spectral Sequence

The mod-p Adams spectral sequence is a spectral sequence built from mod-p cohomology that computes p-completed stable homotopy under its convergence hypotheses. For the sphere its second page is

E_2^(s,t)=Ext_(A_p)^(s,t)(F_p,F_p) ==> pi_(t-s)S_p^ ^ ,

where A_p is the mod-p Steenrod algebra and s is Adams filtration. A permanent cycle determines a class in the associated graded homotopy group, which can have several representatives before passage to that quotient. The stem is t-s, not the internal degree t. The odd-primary Kervaire invariant problem at the prime three concerns a particular family in this spectral sequence.

See also

Odd-Primary Kervaire Invariant Problem, Spectral Sequence, Sphere Spectrum, Steenrod Algebra

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References

Ravenel, D. C. Complex Cobordism and Stable Homotopy Groups of Spheres, 2nd ed. Providence, RI: Amer. Math. Soc., 2003. https://www.sas.rochester.edu/mth/sites/doug-ravenel/mybooks/ravenel.pdf.

Cite this as:

Weisstein, Eric W. "Adams Spectral Sequence." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AdamsSpectralSequence.html

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