Related papers: On the E2-term of the bo-Adams spectral sequence

In the early 2000's, Baues computed the secondary Steenrod algebra, the algebra of all secondary cohomology operations. Together with Jibladze, they showed that this gives an algorithm that computes all Adams $d_2$ differentials for the…

An algorithm is described giving effective determination of the second differential in the Adams spectral sequence. The algorithm is based on the notion of secondary derived functor, and on the explicit algebraic model of the groupoid…

In this paper, we describe a novel way of identifying Adams spectral sequence $E_2$-terms in terms of homological algebra of quiver representations. Our method applies much more broadly than the standard techniques based on…

We study $v_n$-periodic phenomena in $C_2$-equivariant stable homotopy through the lens of the $C_2$-equivariant Adams spectral sequence at the prime 2. In particular, we construct/detect certain classes related to powers of the $v_n$…

We study the mod-2 cohomology spectral sequence arising from delooping the Bousfield-Kan cosimplicial space giving the 2-nilpotent completion of a connective spectrum $X$. Under good conditions its $E_{2}$-term is computable as certain…

We compute the $E_2$ page of the Adams spectral sequence converging to the connective KO-theory of the second mod 2 Eilenberg-MacLane space, $ko_*(K(Z/2,2))$. This required a careful analysis of the structure of $H^*(K(Z/2,2);Z_2)$ as a…

The chromatic spectral sequence is introduced in \cite{mrw} to compute the $E_2$-term of the \ANSS\ for computing the stable homotopy groups of spheres. The $E_1$-term $E_1^{s,t}(k)$ of the spectral sequence is an Ext group of…

Let $E=E_n$ be Morava $E$-theory of height $n$. In previous work Devinatz and Hopkins introduced the $K(n)$-local $E_n$-Adams spectral sequence and showed that, under certain conditions, the $E_2$-term of this spectral sequence can be…

We compute the cohomology of the subalgebra $A^{C_2}(1)$ of the $C_2$-equivariant Steenrod algebra $A^{C_2}$. This serves as the input to the $C_2$-equivariant Adams spectral sequence converging to the $RO(C_2)$-graded homotopy groups of an…

We describe the dualization of the algebra of secondary cohomology operations in terms of generators extending the Milnor dual of the Steenrod algebra. In this way we obtain explicit formulae for the computation of the E_3-term of the Adams…

We present progress in trying to verify a long-standing conjecture by Mark Mahowald on the $v_{1}$-periodic component of the classical Adams spectral sequence for a Moore space $M$. The approach we follow was proposed by John Palmieri in…

We construct a new type of spectral sequences for the mixed Hodge structures on the cohomology of locally symmetric varieties. These spectral sequences converge to the edge components in the Hodge triangles, and the E1-terms are expressed…

We compute the cotorsion product of the mod 2 cohomology of spinor group spin(n), which is the E_2-term of the Rothenberg-Steenrod spectral sequence for the mod 2 cohomology of the classifying space of the spinor group spin(n). As a…

We find out some relations between the classical Adams spectral sequences for stunted real projective spectra, the Borel $C_2$-equivariant Adams spectral sequence for the 2-completed sphere, and the genuine $C_2$-equivariant Adams spectral…

We make some computations in stable motivic homotopy theory over Spec \mathbb{C}, completed at 2. Using homotopy fixed points and the algebraic K-theory spectrum, we construct a motivic analogue of the real K-theory spectrum KO. We also…

The Adams spectral sequence was invented by J.F.Adams almost fifty years ago for calculations of stable homotopy groups of topological spaces and in particular of spheres. The calculation of differentials of this spectral sequence is one of…

Classical homological algebra takes place in additive categories. In homotopy theory such additive categories arise as homotopy categories of ``additive groupoid enriched categories'', in which a secondary analog of homological algebra can…

We compute the $E_2$-term of the Bousfield-Kan spectral sequence converging to the homotopy groups of the semi-cosimplicial $E_{\infty}$ ring spectrum $Q(2)_{(3)}$. This 3-local spectrum was constructed by M. Behrens using degree 2…

We compute the h_1-localized cohomology of the motivic Steenrod algebra over C. This serves as the input to an Adams spectral sequence that computes the motivic stable homotopy groups of the eta-local motivic sphere. We compute some of the…

In previous work of the first author and Jibladze, the $E_3$-term of the Adams spectral sequence was described as a secondary derived functor, defined via secondary chain complexes in a groupoid-enriched category. This led to computations…