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Let $\mathcal A^\ast$ be the (mod 2) Steenrod algebra. Question 1: Is there a classification of homogeneous elements $D \in \mathcal A^n$ such that $D^2 = 0$? Question 2: Is there a classification of ...

Let $//$ denote the Hopf algebra quotient. We know that: $$HF_{2}^*(ko) \simeq A//A(1)$$ $$HF_2^*(tmf) \simeq A//A(2)$$ By Hopf invariant one, we know there is no $X$ such that $HF_2^*(X) \simeq A//...