Volume 21, issue 7 (2021)

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Unstable modules with only the top $k$ Steenrod operations

Zhulin Li

Algebraic & Geometric Topology 21 (2021) 3623–3662

We study an abelian category of unstable modules with the top k Steenrod operations at the prime 2. We show that this category has homological dimension at most k. We establish forgetful functors, suspension functors, loop functors and Frobenius functors between such modules. The forgetful functors induce an inverse system of Ext groups, and the inverse system stabilizes when the covariant module is bounded above. We define an analogue of the Λ algebra in this context and verify that its cohomology computes Ext.

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Steenrod algebra, ringoid, top $k$ operations
Mathematical Subject Classification
Primary: 55S10
Secondary: 55U99
Received: 12 July 2020
Revised: 21 December 2020
Accepted: 7 January 2021
Published: 28 December 2021
Zhulin Li
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States