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arXiv · 1903.10288

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

Andrew Baker·Tilman Bauer
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Abstract

The Joker is an important finite cyclic module over the mod-$2$ Steenrod algebra $\mathcal A$. 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. 2019-10-18. The realizability of some finite-length modules over the Steenrod algebra by spaces. https://doi.org/10.2140/agt.2020.20.2129

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