Cyclic length and chromatic fixed-point loss

Determines the optimal chromatic loss from geometric H-fixed points to geometric G-fixed points for every subgroup H of a finite p-group G. At every nonnegative height, the loss equals the shortest subnormal-chain length from H to G with cyclic quotients. Each quotient counts once regardless of order, and finite spectra witness sharpness.

Manuscript

Cyclic length and chromatic fixed-point loss

September 24, 2026 · source · cite as \cite{OAI:Cyclic-Length-and-Chromatic-Fixed-Point-Loss-September-24-2026}

For a finite p-group G and a subgroup H, we prove that the optimal chromatic fixed-point loss equals the shortest length of a subnormal chain from H to G with cyclic quotients. The equality holds at every prime and every nonnegative height, resolving positively the equality proposed by Kuhn and Lloyd.

Result 314 · Topology. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.