We describe a variant construction of the unstable Adams spectral sequence for space $Y$, associated to any free simplicial resolution $H^*(Y;R)$ $R=\mathbb{F}_p$ or $\mathbb{Q}$. use this differentials and filtration in terms appropriate systems higher cohomology operations.

Bott’s periodicity theorem is applied to calculate higher-order differentials of the Adams spectral sequence of homotopy groups π∗(SO). The resulting formulas are used to find higher-order differentials of the Adams spectral sequence of homotopy groups of spheres. DOI: 10.1134/S0001434608110126

abutting to the stable homotopy of X. It has long been recognized that a map A +B of ring-spectra gives rise to information about the differentials in this spectral sequence. The main purpose of this paper is to prove a systematic theorem in this direction, and give some applications. To fix ideas, let p be a prime number, and take B to be the modp EilenbergMacLane spectrum H and A to be the Br...

I t has been long known that the cohomology H (A) of the mod 2 Steenrod algebra A admits squaring operations. (For example, see [ó].) Since H(A) is isomorphic to the £2 term of the mod 2 Adams spectral sequence [2], it is natural to inquire as to the relation of these squaring operations to the structure of the Adams spectral sequence. In this note we announce some results of this type extendin...

The Telescope Conjecture (made public in a lecture at Northwestern University in 1977) says that the vn–periodic homotopy of a finite complex of type n has a nice algebraic description. It also gives an explicit description of certain Bousfield localizations. In this paper we outline a proof that it is false for n = 2 and p ≥ 5. A more detailed account of this work will appear in [Rav]. In view...

The goal of this work is the construction of the analogue to the Adams spectral sequence in cobordism theory, calculation of the ring of cohomology operations in this theory, and also a number of applications: to the problem of computing homotopy groups and the classical Adams spectral sequence, fixed points of transformations of period p, and others.

Let p be an odd prime and A be the mod p Steenrod algebra. For computing the stable homotopy groups of spheres with the classical Adams spectral sequence, we must compute the E2 -term of the Adams spectral sequence, Ext A ( p, p) . In this paper we prove that in the cohomology of A , the product k0hnδ̃s+4 ∈ Ext s+7,t(s,n)+s A ( p, p) , is nontrivial for n ≥ 5, and trivial for n = 3, 4, where δ̃s+...

Let A be the mod p Steenrod algebra and S the sphere spectrum localized at p, where p is an odd prime. In 2001 Lin detected a new family in the stable homotopy of spheres which is represented by (b0hn − h1bn−1) ∈ Ext n+p)q A (Zp,Zp) in the Adams spectral sequence. At the same time, he proved that i∗(h1hn) ∈ Ext +p)q A (H ∗M,Zp) is a permanent cycle in the Adams spectral sequence and converges t...

In this paper, some groups Ext A (Zp, Zp) with specialized s and t are first computed by the May spectral sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s+5 in the stable homotopy groups of spheres πpnq+(s+3)pq+(s+1)q−5S which is represented (up to a nonzero scalar) by β̃s+2b0hn ∈ Ext q+(s+3)pq+(s+1)q+s A (Zp, Zp) in the ...