The realizability of some finite-length modules over the Steenrod algebra by spaces

Baker, A. and Bauer, T. (2020) The realizability of some finite-length modules over the Steenrod algebra by spaces. Algebraic and Geometric Topology, 20(4), pp. 2129-2143. (doi: 10.2140/agt.2020.20.2129)

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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.

Item Type:Articles
Additional Information:The first author would like to thank the following: The Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme Homotopy Harnessing Higher Structures when work on this paper was undertaken (this work was supported by EPSRC grant number EP/R014604/1); Kungliga Tekniska H ̈ogskolan and Stockholms Universitet for supporting a visit by A. Baker in Spring of 2018.
Glasgow Author(s) Enlighten ID:Baker, Dr Andrew
Authors: Baker, A., and Bauer, T.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Research Group:Geometry & Topology
Journal Name:Algebraic and Geometric Topology
Publisher:Mathematical Sciences Publishers
ISSN (Online):1472-2739
Published Online:20 July 2020
Copyright Holders:Copyright © 2020 Mathematical Sciences Publishers
First Published:First published in Algebraic and Geometric Topology 20(4): 2129-2143
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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