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Smith-Toda Complex

A Smith-Toda complex V(n) at a prime p is a finite p-local spectrum whose Brown-Peterson homology is

BP_*V(n)=BP_*/(p,v_1,...,v_n),

as a graded BP_*BP-comodule with the canonical quotient coaction and generator in degree zero. This is a realization condition on a finite spectrum, not merely a formal quotient of a polynomial ring.

See also

Brown-Peterson Spectrum, Morava K-Theory, Topological Spectrum

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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. "Smith-Toda Complex." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Smith-TodaComplex.html

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