On the metastable homotopy of mod 2 Moore spaces

TL;DR

This paper investigates the metastable homotopy groups of mod 2 Moore spaces, establishing that their double loop spaces and homotopy groups have exponent 4 within a certain range, advancing understanding of their algebraic structure.

Contribution

It provides new results on the exponents of metastable homotopy groups of mod 2 Moore spaces, specifically showing they have exponent 4 below a certain connectivity threshold.

Findings

Double loop space of 4n-dimensional mod 2 Moore spaces has exponent 4.

Homotopy groups of 4n-dimensional mod 2 Moore spaces have exponent 4.

Results apply below four times the connectivity range.

Abstract

In this article, we study the exponents of metastable homotopy of mod $2$ Moore spaces. Our result gives that the double loop space of $4n$-dimensional mod $2$ Moore spaces has a multiplicative exponent $4$ below the range of $4$ times the connectivity. As a consequence, the homotopy groups of $4n$-dimensional mod $2$ Moore spaces have an exponent $4$ below the range of $4$ times the connectivity.