# On the cohomology of the mod-2 Steenrod algebra and the non-existence of elements of Hopf invariant one

@article{Wang1967OnTC, title={On the cohomology of the mod-2 Steenrod algebra and the non-existence of elements of Hopf invariant one}, author={John S. P. Wang}, journal={Illinois Journal of Mathematics}, year={1967}, volume={11}, pages={480-490} }

BY JOHI S. P. 6 A very handy E term of the Adams spectral sequence for the sphere spectrum is obtained in [5]. Here we shall use it to calculate the cohomology of the mod-2 Steenrod algebra Hs’t(A) in the range s _< 3 and find some relations among the hi’s and c.’s in the range s <_ 4. The structure of H3’t(A)and the relations h0 h 0 for i _> 4 yield the information d2hi ho hi_lfori_> 4 by an easy induction starting from dh4 ho h. Hence a new proof for the non-existence of the elements of Hopf…

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