On the metastable homotopy of mod 2 Moore spaces

Mikhailov, Roman; Wu, Jie

doi:10.2140/agt.2016.16.1773

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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

DOI: 10.2140/agt.2016.16.1773

Abstract

We study the exponents of metastable homotopy of mod $2$ Moore spaces. We prove that the double loop space of $4 n$ –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 $4 n$ –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

Volume 16, issue 3 (2016)