Algebraic EHP sequences

TL;DR

This paper provides a new proof for the existence of algebraic EHP sequences related to the homotopy groups of spheres, connecting geometric fibrations with algebraic Ext group sequences via the Lambda algebra.

Contribution

It introduces an alternative proof for the algebraic EHP sequences, linking geometric and algebraic methods in homotopy theory.

Findings

Establishes the existence of long exact sequences of Ext groups

Connects geometric EHP sequences with algebraic Ext sequences

Provides a new proof technique for the algebraic EHP phenomenon

Abstract

The James fibrations give rise to the geometric EHP sequences of homotopy groups of spheres. Using techniques from the Lambda algebra, \cite{BCKQRS66} shows that there are similar long exact sequences of Ext groups defining the $E_{2}-$page of the Bousfield-Kan spectral sequence (also known as the unstable Adams spectral sequence) computing homotopy groups of spheres. In this paper, we give another proof for this phenomenon.