In [1], Miller, Ravenel and Wilson defined generalized beta elements in the E2-term of the Adams-Novikov spectral sequence converging to the stable homotopy groups of spheres, and in [5], Oka showed that the beta elements of the form βtp2/r for positive integers t and r survives to the stable homotopy groups at a prime p > 3, when r ≤ 2p − 2 and r ≤ 2p if t > 1. In this paper, we expand the con...

Through an investigation of properties of Chern classes, Quillen discovered a connection between stable homotopy theory and 1-dimensional formal group laws [31]. After almost 40 years, the impacts of this connection are still being felt. The stratification of formal group laws in finite characteristic gives rise to the chromatic filtration in stable homotopy theory [32], and has definite calcul...

English Translation of Chapter 9 of the book Adams spectral sequence and stable homotopy groups of spheres (In Chinese)