On the metastable homotopy of mod $2$ Moore spaces

Abstract

We study the exponents of metastable homotopy of mod $2$ Moore spaces. We prove 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 of $4$ below the range of $4$ times the connectivity.