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.
Keywords: stable homotopy theory, Steenrod algebra
Baker, Andrew 1 ; Bauer, Tilman 2
@article{10_2140_agt_2020_20_2129,
author = {Baker, Andrew and Bauer, Tilman},
title = {The realizability of some finite-length modules over the {Steenrod} algebra by spaces},
journal = {Algebraic and Geometric Topology},
pages = {2129--2143},
year = {2020},
volume = {20},
number = {4},
doi = {10.2140/agt.2020.20.2129},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2020.20.2129/}
}
TY - JOUR AU - Baker, Andrew AU - Bauer, Tilman TI - The realizability of some finite-length modules over the Steenrod algebra by spaces JO - Algebraic and Geometric Topology PY - 2020 SP - 2129 EP - 2143 VL - 20 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2020.20.2129/ DO - 10.2140/agt.2020.20.2129 ID - 10_2140_agt_2020_20_2129 ER -
%0 Journal Article %A Baker, Andrew %A Bauer, Tilman %T The realizability of some finite-length modules over the Steenrod algebra by spaces %J Algebraic and Geometric Topology %D 2020 %P 2129-2143 %V 20 %N 4 %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2020.20.2129/ %R 10.2140/agt.2020.20.2129 %F 10_2140_agt_2020_20_2129
Baker, Andrew; Bauer, Tilman. The realizability of some finite-length modules over the Steenrod algebra by spaces. Algebraic and Geometric Topology, Tome 20 (2020) no. 4, pp. 2129-2143. doi: 10.2140/agt.2020.20.2129
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