Geodesic
A NOTE ON A-ANNIHILATED GENERATORS OF H*QX
Glasgow mathematical journal, Tome 62 (2020) no. 2, pp. 281-295

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DOI

For a path connected space X, the homology algebra $H_*(QX; \mathbb{Z}/2)$ is a polynomial algebra over certain generators QIx. We reinterpret a technical observation, of Curtis and Wellington, on the action of the Steenrod algebra A on the Λ algebra in our terms. We then introduce a partial order on each grading of H*QX which allows us to separate terms in a useful way when computing the action of dual Steenrod operations $Sq^i_*$ on $H_*(QX; \mathbb{Z}/2)$. We use these to completely characterise the A-annihilated generators of this polynomial algebra. We then propose a construction for sequences I so that QIx is A-annihilated. As an application, we offer some results on the form of potential spherical classes in H*QX upon some stability condition under homology suspension. Our computations provide new numerical conditions in the context of hit problem. 
ZARE, HADI. A NOTE ON A-ANNIHILATED GENERATORS OF H*QX. Glasgow mathematical journal, Tome 62 (2020) no. 2, pp. 281-295. doi: 10.1017/S0017089519000090
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     title = {A {NOTE} {ON} {A-ANNIHILATED} {GENERATORS} {OF} {H*QX}},
     journal = {Glasgow mathematical journal},
     pages = {281--295},
     year = {2020},
     volume = {62},
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     doi = {10.1017/S0017089519000090},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089519000090/}
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