The Adams spectral sequence was invented by J.F.Adams [1] 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 the most difficult problem of Algebraic Topology. Here we consider an approach to solve this problem in the case of Z/2 coefficients and find inductive ...

A localisation of the category of n-manifolds is introduced by formally inverting the connected sum construction with a chosen nmanifold Y . On the level of automorphism groups, this leads to the stable diffeomorphism groups of n-manifolds. In dimensions 0 and 2, this is connected to the stable homotopy groups of spheres and the stable mapping class groups of Riemann surfaces. In dimension 4 th...

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...