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Infinite families of higher torsion in the homotopy groups of Moore spaces

Steven Amelotte, Frederick R Cohen and Yuxin Luo

Algebraic & Geometric Topology 23 (2023) 2389–2414
Abstract

We give a refinement of the stable Snaith splitting of the double loop space of a Moore space and use it to construct infinite periodic families of elements of order pr+1 in the homotopy groups of mod pr Moore spaces. For odd primes p, our splitting implies that the homotopy groups of the mod pr+1 Moore spectrum are summands of the unstable homotopy groups of each mod pr Moore space.

Keywords
Moore space, unstable homotopy, Bockstein spectral sequence, periodic homotopy groups
Mathematical Subject Classification
Primary: 55P35, 55P42, 55Q51, 55Q52
References
Publication
Received: 24 November 2021
Revised: 26 February 2022
Accepted: 6 March 2022
Published: 25 July 2023
Authors
Steven Amelotte
Department of Mathematics
Western University
London, ON
Canada
Frederick R Cohen
Department of Mathematics
University of Rochester
Rochester, NY
United States
Yuxin Luo
Department of Mathematics
University of Rochester
Rochester, NY
United States

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