학술논문
The realizability of some finite-length modules over the Steenrod algebra by spaces
Document Type
Working Paper
Author
Source
Algebr. Geom. Topol. 20 (2020) 2129-2143
Subject
Language
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.
Comment: 11 pages, to appear in Algebraic and Geometric Topology
Comment: 11 pages, to appear in Algebraic and Geometric Topology