2-local unstable homotopy groups of indecomposable $\mathbf{A}_3^2$ -complexes

TL;DR

This paper computes the 2-local unstable homotopy groups of specific indecomposable complexes using homotopy analysis of a related construction, advancing understanding of their algebraic topology.

Contribution

It introduces a method for calculating homotopy groups of indecomposable complexes via analysis of the homotopy property of J(X,A).

Findings

Calculated 2-local unstable homotopy groups for the complexes.

Established a link between homotopy properties of J(X,A) and the complexes.

Provided new tools for studying homotopy groups of complex spaces.

Abstract

In this paper, we calculate the 2-local unstable homotopy groups of indecomposable $\mathbf{A}_3^2$-complexes. The main technique used is analysing the homotopy property of $J(X,A)$, defined by B. Gray for a CW-pair $(X,A)$, which is homotopy equivalent to the homotopy fibre of the pinch map $X\cup CA\rightarrow \Sigma A$.