3 problems

Matching

Curtis conjecture on spherical classes in $H_*QS^0$
About 11 years old
Curtis conjecture. Only the Hopf invariant one and Kervaire invariant one elements survive under $h$ .
openspherical-classes stable-homotopy-theory
023
Eccles's conjecture on spherical classes and detection by homology operations
At least 10 years old
Eccles conjecture. Under these hypotheses, the stable adjoint of $f$ either is detected by homology or is detected by a primary operation in its mapping cone.
openspherical-classes stable-homotopy-theory
010
Conjecture on the suspension-kernel classes generated by $[\eta_i]_6$
About 17 years old
Suspension-kernel conjecture. The class $[\eta_i]_6$ dies under $\sigma_*$ . Consequently, the subalgebra of $H_*Q_0S^{-2^i+6}$ generated by the classes $Q^I[\eta_i]_6$ belongs to…
openhomology-of-infinite-loop-spaces spherical-classes stable-homotopy-theory
07

Curtis conjecture on spherical classes in H∗QS0H_*QS^0H∗​QS0