Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the form of potential spherical classes in $H_*Q_0S^0$   This note is about spherical classes in $H_*Q_0S^0$. A conjecture, due to Ed.
Curtis, predicts that only Hopf invariant one and Kervaire invariant one
elements will give rise to spherical classes in $H_*Q_0S^0$. Yet, there has
been no proof of this conjecture around. Assuming that this conjecture fails,
there must exist some other spherical classes in $H_*Q_0S^0$. This note
determines the form of these potential spherical classes, and sets the target
for someone who wishes to prove the conjecture, in the sense that correctness
of the Curtis conjecture will be the same as failure of any classes predicted
in this paper being spherical.

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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: eess