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Chromatic Fixed-Point Loss

Chromatic fixed-point loss for H<=G, with G a finite p-group, is the least nonnegative integer r_n(G,H) such that

K(n+r_n(G,H))_*Phi^HX=0 ==> K(n)_*Phi^GX=0

for every finite p-local genuine G-spectrum X. Here Phi^H denotes geometric fixed points and n>=0, with K(0) interpreted as rational homology. Geometric fixed points remove contributions induced from proper subgroups before taking fixed points.

See also

Cyclic Length, Morava K-Theory, Topological Spectrum

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References

Kuhn, N. J. and Lloyd, C. J. R. "Chromatic Fixed Point Theory and the Balmer Spectrum for Extraspecial 2-Groups." Amer. J. Math. 146, 769-812, 2024. https://doi.org/10.1353/ajm.2024.a928325.

Cite this as:

Weisstein, Eric W. "Chromatic Fixed-Point Loss." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ChromaticFixed-PointLoss.html

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