A conjecture of may on E2-term of the may spectral sequence for the cohomology of the steenrod algebra

1990 ◽  
pp. 15-52
Author(s):  
Wen-Hsiung Lin
Keyword(s):  
Spectral Sequence ◽  
Steenrod Algebra ◽  
May Spectral Sequence

The Convergence of Some Products in the Adams Spectral Sequence

2015 ◽  
Vol 117 (2) ◽  
pp. 304
Author(s):  
Yuyu Wang ◽  
Jianbo Wang
Keyword(s):  
Spectral Sequence ◽  
Adams Spectral Sequence ◽  
May Spectral Sequence ◽  
Related Family ◽  
The Family

In this paper, we will use the family of homotopy elements $\zeta_n\in\pi_*S$, represented by $h_0b_n\in \operatorname{Ext}_A^{3,p^{n+1} q+q}(\mathsf{Z}_p, \mathsf{Z}_p)$ in the Adams spectral sequence, to detect a $\zeta_n$-related family $\gamma_{s+3}\beta_2\zeta_{n-1}$ in $\pi_*S$. Our main methods are the Adams spectral sequence and the May spectral sequence, here prime $p\geq 7$, $n>3$, $q=2(p-1)$.

On the differentials in the Adams spectral sequence

1964 ◽  
Vol 60 (3) ◽  
pp. 409-420 ◽  
Author(s):  
C. R. F. Maunder
Keyword(s):  
Spectral Sequence ◽  
Higher Order ◽  
Adams Spectral Sequence ◽  
Steenrod Algebra ◽  
Stable Homotopy ◽  
Homotopy Groups ◽  
Homotopy Groups Of Spheres ◽  
Stable Homotopy Groups ◽  
Cohomology Operations ◽  
Image Position

In this paper, we shall prove a result which identifies the differentials in the Adams spectral sequence (see (1,2)) with certain cohomology operations of higher kinds, in the sense of (4). This theorem will be stated precisely at the end of section 2, after a summary of the necessary information about the Adams spectral sequence and higher-order cohomology operations; the proof will follow in section 3. Finally, in section 4, we shall consider, by way of example, the Adams spectral sequence for the stable homotopy groups of spheres: we show how our theorem gives a proof of Liulevicius's result that , where the elements hn (n ≥ 0) are base elements ofcorresponding to the elements Sq2n in A, the mod 2 Steenrod algebra.

scholarly journals Detection of a new nontrivial family in the stable homotopy of spheres $ \mbf{\pi_{\ast}S} $

2008 ◽  
Vol 39 (1) ◽  
pp. 75-83
Author(s):  
Liu Xiugui ◽  
Jin Yinglong
Keyword(s):  
Spectral Sequence ◽  
Homotopy Theory ◽  
Steenrod Algebra ◽  
Stable Homotopy ◽  
Homotopy Groups ◽  
Nontrivial Element ◽  
Homotopy Groups Of Spheres ◽  
Stable Homotopy Groups ◽  
Stable Homotopy Of Spheres ◽  
Gamma S

To determine the stable homotopy groups of spheres is one of the central problems in homotopy theory. Let $ A $ be the mod $ p $ Steenrod algebra and $S$ the sphere spectrum localized at an odd prime $ p $. In this article, it is proved that for $ p\geqslant 7 $, $ n\geqslant 4 $ and $ 3\leqslant s $, $ b_0 h_1 h_n \tilde{\gamma}_{s} \in Ext_A^{s+4,\ast}(\mathbb{Z}_p,\mathbb{Z}_p) $ is a permanent cycle in the Adams spectral sequence and converges to a nontrivial element of order $ p $ in the stable homotopy groups of spheres $ \pi_{p^nq+sp^{2}q+(s+1)pq+(s-2)q-7}S $, where $ q=2(p-1 ) $.

scholarly journals Motivic connective K-theories and the cohomology of A(1)

2011 ◽  
Vol 7 (3) ◽  
pp. 619-661 ◽  
Author(s):  
Daniel C. Isaksen ◽  
Armira Shkembi
Keyword(s):  
Spectral Sequence ◽  
Fixed Points ◽  
Homotopy Theory ◽  
Steenrod Algebra ◽  
The Real ◽  
Special Cases ◽  
Ext Groups ◽  
Motivic Homotopy Theory ◽  
Motivic Homotopy ◽  
Homotopy Fixed Points

AbstractWe make some computations in stable motivic homotopy theory over Spec ℂ, completed at 2. Using homotopy fixed points and the algebraic K-theory spectrum, we construct over ℂ a motivic analogue of the real K-theory spectrum KO. We also establish a theory of motivic connective covers over ℂ to obtain a motivic version of ko. We establish an Adams spectral sequence for computing motivic ko-homology. The E2-term of this spectral sequence involves Ext groups over the subalgebra A(1) of the motivic Steenrod algebra. We make several explicit computations of these E2-terms in interesting special cases.

scholarly journals On May spectral sequence and the algebraic transfer

2011 ◽  
Vol 138 (1-2) ◽  
pp. 141-160 ◽  
Author(s):  
Phan Hoàng Chơn ◽  
Lê Minh Hà
Keyword(s):  
Spectral Sequence ◽  
May Spectral Sequence
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