Volume 16, issue 3 (2016)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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
References
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