# On the Non-Existence of Elements of Hopf Invariant One

@article{Adams1960OnTN,
title={On the Non-Existence of Elements of Hopf Invariant One},
journal={Annals of Mathematics},
year={1960},
volume={72},
pages={20}
}
• Published 1 July 1960
• Mathematics
• Annals of Mathematics
721 Citations
SOME GENERIC DEGREES AND ITS APPLICATION
Let A denote the Steenrod algebra at the prime 2 and let k = Z2. An open problem of homotopy theory is to determine a minimal set of A-generators for the polynomial ring Pq = k[x1, . . . , xq] = H(k,
Structure of the space of $GL_4(\mathbb Z_2)$-coinvariants $\mathbb Z_2\otimes_{GL_4(\mathbb Z_2)} PH_*(\mathbb Z_2^4, \mathbb Z_2)$ in some generic degrees and its application to Singer's cohomological transfer
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The Arf-Kervaire Invariant Problem in Algebraic Topology: Introduction
• Mathematics
• 2010
This paper gives the history and background of one of the oldest problems in algebraic topology, along with an outline of our solution to it. A rigorous account can be found in our preprint [HHR].

## References

SHOWING 1-10 OF 18 REFERENCES
NON-PARALLELIZABILITY OF THE n-SPHERE FOR n > 7.
• M. Kervaire
• Mathematics, Medicine
Proceedings of the National Academy of Sciences of the United States of America
• 1958
On the parallelizability of the spheres
• Mathematics
• 1958
is always divisible by (2k — 1)!. I wonder if you have noted the connection of this result with classical problems, such as the existence of division algebras, and the parallelizability of spheres.
On the structure and applications of the steenrod algebra
Nutzungsbedingungen Mit dem Zugriff auf den vorliegenden Inhalt gelten die Nutzungsbedingungen als akzeptiert. Die angebotenen Dokumente stehen für nicht-kommerzielle Zwecke in Lehre, Forschung und
THE STEENROD ALGEBRA AND ITS DUAL1
1. Summary Let 57 * denote the Steenrod algebra corrresponding to an odd prime p. (See ? 2 for definitions.) Our basic results (? 3) is that 5i* is a Hopf
ON THE COBAR CONSTRUCTION.