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The realizability of
some finite-length modules over the Steenrod algebra by
spaces
Andrew Baker and Tilman Bauer |
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Algebraic & Geometric Topology 20 (2020) 2129–2143
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Abstract |
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The Joker is an important finite cyclic module over the mod- Steenrod algebra . 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 (–compact groups, topological modular forms) and may be of independent interest. |
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Keywords
stable homotopy theory, Steenrod algebra
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Mathematical Subject Classification 2010
Primary: 55P42
Secondary: 55S10, 55S20
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References |
Publication
Received: 29 May 2019
Revised: 12 September 2019
Accepted: 17 October 2019
Published: 20 July 2020
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Authors |
| Andrew Baker | |
| School of Mathematics and
Statistics University of Glasgow Glasgow United Kingdom |
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| http://www.maths.gla.ac.uk/~ajb | |
| Tilman Bauer | |
| Institutionen för Matematik Kungliga Tekniska Högskolan Stockholm Sweden |
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| https://people.kth.se/~tilmanb | |
