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Arf's conjecture on dimensions admitting nontrivial Arf-Kervaire invariant
Arf's conjecture. Elements $\Theta_n$ having nontrivial Arf-Kervaire invariant can exist only for
Conjectureopenarf-kervaire-invariant stable-homotopy-theoryarXiv posted 2 days ago
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The nonexistence of an Arf-Kervaire invariant one element in the 126-stem
The 126-stem Arf-Kervaire conjecture. There is no element in
Conjectureopenarf-kervaire-invariant stable-homotopy-theoryarXiv posted 2 days ago
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Barratt-Jones-Mahowald conjecture on Arf-Kervaire invariant one
Barratt-Jones-Mahowald conjecture. This condition is equivalent to the composition of $\Theta$ with the Kahn–Priddy map having Arf-Kervaire invariant one.
Conjectureopenarf-kervaire-invariant stable-homotopy-theoryarXiv posted 2 days ago

Arf's conjecture on dimensions admitting nontrivial Arf-Kervaire invariant