#### Volume 16, issue 3 (2016)

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On the metastable homotopy of mod $2$ Moore spaces

### Roman Mikhailov and Jie Wu

Algebraic & Geometric Topology 16 (2016) 1773–1797
##### 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.

##### Keywords
Moore space, Cohen group, homotopy groups, homotopy exponent, metastable homotopy, loop space
##### Mathematical Subject Classification 2010
Primary: 55Q52, 14F35, 55Q20
Secondary: 55Q05, 55P35