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Curtis Conjecture

The Curtis conjecture asserts that the positive-degree image of the stable mod-two Hurewicz homomorphism

pi_d^S->H_d(Q_0S^0;F_2)

is spanned by the Hopf invariant one classes and the Kervaire invariant one classes that exist. Here Q_0S^0 is the basepoint component of the infinite loop space of the sphere spectrum. The Hopf classes are eta, nu, and sigma, in stems 1, 3, and 7. The Kervaire classes theta_j, when they exist, have stem 2^(j+1)-2.

See also

Hopf Invariant One Theorem, Sphere Spectrum, Stable Homotopy Group

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References

Zare, H. "On Spherical Classes in H_*QX." 6 Jan 2011. https://arxiv.org/abs/1101.1215.

Cite this as:

Weisstein, Eric W. "Curtis Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CurtisConjecture.html

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