Related papers: An extension in the Adams spectral sequence in dim…

We describe a variant construction of the unstable Adams spectral the sequence for a space $Y$, associated to any free simplicial resolution of $H^*(Y;R)$ for $R=\mathbb{F}_p$ or $\mathbb{Q}$. We use this construction to describe the…

We show that there is a non-trivial differential $d_4(h_6^3) =h_0^3g_4$ in the mod 2 Adams spectral sequence for spheres. This together with the results in \cite{barratt_differentials_1970,lin_differential_1998,kan_differential_2001}…

We develop the theory of anomalous elasticity in two-dimensional flexible materials with orthorhombic crystal symmetry. Remarkably, in the universal region, where characteristic length scales are larger than the rather small Ginzburg scale…

We bootstrap the $4$-point amplitude of $\mathcal{N}=2$ hypermultiplets in $\text{AdS}_2 \times \text{S}^2$ at tree-level and for arbitrary external weights. We hereby explicitly demonstrate the existence of a hidden four-dimensional…

In this article we show that the $p$-torsion exponent of the stable stems grows sublinearly in $n$ and the $p$-rank of the $E_2$-page of the Adams spectral sequence grows as $\exp(\Theta( \log(n)^3))$. Together these bounds provide the…

For groups of prime order, equivariant stable maps between equivariant representation spheres are investigated using the Borel cohomology Adams spectral sequence. Features of the equivariant stable homotopy category, such as stability and…

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 characterize the 2-line of the p-local Adams-Novikov spectral sequence in terms of modular forms satisfying a certain explicit congruence condition for primes p > 3. We give a similar characterization of the 1-line, reinterpreting some…

The Adams spectral sequence was invented by J.F.Adams 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 the…

We revisit methods of proof of the Adams Conjecture in order to correct and supplement earlier efforts to prove analogous conjectures in the stable homotopy category. We utilize simplicial schemes over an algebraically closed field of…

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…

In this note, we confirm a conjecture of Larson that arises in the Adams--Novikov spectral sequence (ANSS) for the stable homotopy groups of spheres and, specifically, in Behrens' program on explicit modular forms detecting $v_2$--periodic…

We use obstruction theory based on the unstable Adams spectral sequence to construct self maps of finite quaternionic projective spaces. As a result, a conjecture of Feder and Gitler regarding the classification of self maps up to homology…

We introduce the category Pstem[n] of n-stems, with a functor P[n] from spaces to Pstem[n]. This can be thought of as the n-th order homotopy groups of a space. We show how to associate to each simplicial n-stem Q an (n+1)-truncated…

Using techniques in motivic homotopy theory, especially the theorem of Gheorghe, the second and the third author on the isomorphism between motivic Adams spectral sequence for $C{\tau}$ and the algebraic Novikov spectral sequence for…

We show that the spectral sequence converging to the stable homotopy groups of spheres, induced by the Betti realization of the slice tower for the motivic sphere spectrum, agrees with the Adams-Novikov spectral sequence, after a suitable…

Mahowald's conjecture arose as part of a program attempting to view chromatic phenomena in stable homotopy theory through the lens of the classical Adams spectral sequence. The conjecture predicts the existence of nonzero classes in the…

A colleague asked about the Adams filtrations of the homotopy classes in the homotopy of the fiber of a particular map between GEMs. The theorem proved in arXiv:2105.02601v3 [math.AT] proves to be effective in answering this (Theorem 4.4).…

This paper contains a complete computation of the homotopy ring of the spectrum of topological modular forms constructed by Hopkins and Miller. The computation is done away from 6, and at the (interesting) primes 2 and 3 separately, and in…

In this paper, we determine the 3-cell skeleton of $F$, where $F$ is the homotopy fiber of the canonical pinch map from a suspension of a simply-connected 2-cell complex onto a sphere. The main result is stated $p$-locally: for $p=2$, and…