#### 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
##### Publication
Received: 2 June 2015
Revised: 20 September 2015
Accepted: 13 October 2015
Published: 1 July 2016
##### Authors
 Roman Mikhailov Chebyshev Laboratory St. Petersburg State University 14th Line 29b St. Petersburg 199178 Russia St. Petersburg Department of Steklov Mathematical Institute Jie Wu Department of Mathematics National University of Singapore 10 Lower Kent Ridge Road Singapore 119076 http://www.math.nus.edu.sg/~matwujie