English translation of chapter 9 of the book "Adams spectral sequence and stable homotopy groups of spheres" by Jijkun Lin (In Chinese)(Sciences Press, Beijing 2007)

TL;DR

This paper provides an English translation of a chapter from Lin's book, detailing the discovery of new indecomposable families in stable homotopy groups of spheres using the Adams spectral sequence.

Contribution

It introduces several new indecomposable families in stable homotopy groups, expanding understanding of their structure through detailed detection methods.

Findings

Identification of new indecomposable families such as h_0h_n and h_nb_n

Proofs based on multiple published works by the author

Enhancement of the algebraic understanding of stable homotopy groups

Abstract

This paper is an English translation of chapter nine of the book "Adams spectral sequence and stable homotopy groups of spheres" by Jinkun Lin (in Chinese)(Sciences Press, Beijing 2007). In this paper, a sequence of new indecomposable families in the stable homotopy groups of spheres such as h_0h_n,h_nb_n,h_0h_nh_m,h_0(h_mb_{n-1}-b_{m-1}h_n) families was detected. The proof of all the detections was stated in this paper in based on several published papers by the author.