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2020 The realizability of some finite-length modules over the Steenrod algebra by spaces
Andrew Baker, Tilman Bauer
Algebr. Geom. Topol. 20(4): 2129-2143 (2020). DOI: 10.2140/agt.2020.20.2129

Abstract

The Joker is an important finite cyclic module over the mod-2 Steenrod algebra 𝒜. We show that the Joker, its first two iterated Steenrod doubles, and their linear duals are realizable by spaces of as low a dimension as the instability condition of modules over the Steenrod algebra permits. This continues and concludes prior work by the first author and yields a complete characterization of which versions of Jokers are realizable by spaces or spectra and which are not. The constructions involve sporadic phenomena in homotopy theory (2–compact groups, topological modular forms) and may be of independent interest.

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Andrew Baker. Tilman Bauer. "The realizability of some finite-length modules over the Steenrod algebra by spaces." Algebr. Geom. Topol. 20 (4) 2129 - 2143, 2020. https://doi.org/10.2140/agt.2020.20.2129

Information

Received: 29 May 2019; Revised: 12 September 2019; Accepted: 17 October 2019; Published: 2020
First available in Project Euclid: 1 August 2020

zbMATH: 07226713
MathSciNet: MR4127092
Digital Object Identifier: 10.2140/agt.2020.20.2129

Subjects:
Primary: 55P42
Secondary: 55S10, 55S20

Rights: Copyright © 2020 Mathematical Sciences Publishers

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