Algebraic & Geometric Topology

On the metastable homotopy of mod $2$ Moore spaces

Roman Mikhailov and Jie Wu

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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.

Article information

Algebr. Geom. Topol., Volume 16, Number 3 (2016), 1773-1797.

Received: 2 June 2015
Revised: 20 September 2015
Accepted: 13 October 2015
First available in Project Euclid: 28 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55Q52: Homotopy groups of special spaces 14F35: Homotopy theory; fundamental groups [See also 14H30] 55Q20: Homotopy groups of wedges, joins, and simple spaces
Secondary: 55Q05: Homotopy groups, general; sets of homotopy classes 55P35: Loop spaces

Moore space Cohen group homotopy groups homotopy exponent metastable homotopy loop space


Mikhailov, Roman; Wu, Jie. On the metastable homotopy of mod $2$ Moore spaces. Algebr. Geom. Topol. 16 (2016), no. 3, 1773--1797. doi:10.2140/agt.2016.16.1773.

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