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}
}
  • John S. P. Wang
  • Published 1 September 1967
  • Mathematics
  • Illinois Journal of Mathematics
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… 
The cohomology of the mod 2 Steenrod algebra
A minimal resolution of the mod 2 Steenrod algebra in the range 0 ≤ s ≤ 128, 0 ≤ t ≤ 184, together with chain maps for each cocycle in that range and for the squaring operation Sq0 in the cohomology
The squaring operation on -generators of the Dickson algebra†.
Abstract We study the squaring operation Sq0 on the dual of the minimal -generators of the Dickson algebra. We show that this squaring operation is isomorphic on its image. We also give vanishing
The algebraic EHP sequence
Let A be the dual of the mod-2 Steenrod algebra. If M, N, are graded unstable .4-comodules, one can define and compute the derived functors Coext^M, N) using unstable injective resolutions of N.
The Wedge Family Of The Cohomology Of The C-Motivic Steenrod Algebra
THE WEDGE FAMILY OF THE COHOMOLOGY OF THE C-MOTIVIC STEENROD ALGEBRA by HIEU THAI August 2020 Advisor: Dr. Daniel Isaksen Major: Mathematics Degree: Doctor of Philosophy Computing the stable homotopy
The minimal model for the Batalin–Vilkovisky operad
The purpose of this paper is to explain and to generalize, in a homotopical way, the result of Barannikov–Kontsevich and Manin, which states that the underlying homology groups of some
The motivic lambda algebra and motivic Hopf invariant one problem
We introduce the F -motivic lambda algebra for any field F of characteristic not equal to 2. This is an explicit differential graded algebra whose homology is the E2-page of the F -motivic Adams
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,
SPHERICAL CLASSES AND THE DICKSON ALGEBRA
We attack the conjecture that the only spherical classes in the homology of Q 0 S 0 are Hopf invariant one and Kervaire invariant one elements. We do this by computing products in the E 2 -term of
A Novice's guide to the adams-novikov spectral sequence
Ever since its introduction by J. F. Adams [8] in 1958, the spectral sequence that bears his name has been a source of fascination to homotopy theorists. By glancing at a table of its structure in
Koszul Duality for Associative Algebras
A minimal model for the associative algebra A is a quasi-free resolution (T(W),d) such that the differential map d maps W into ⊕ n≥2 W ⊗n . We would like to find a method to construct this minimal
...
1
2
3
4
5
...

References

SHOWING 1-7 OF 7 REFERENCES
Homologie nicht-additiver Funktoren
  • Anwendungen, Ann. Inst. Fourier (Grenoble)
  • 1961
+ -2' 18
  • forj _>
An unstable Adams spectral sequence, Topology, to appear