A categorical approach to interactions between mod 2 power operations

We generalize the numerical formula due to Nishida which computes the effect of interchanging dual Steenrod operations and Dyer-Lashof operations acting on the homology of a space to a categorical relation between their A-based analogues over any given multiplicative cohomology theory A. Our approach interprets these two power operations as arising from comonadic and monadic structures on the homotopy category of A-modules. This perspective has the advantage of clearly identifying the computational input required to understand the interactions between these operations in concrete terms, given the choice of A—a feature not made explicit in previous work.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Zhu, Heyi

Contributors dc:contributor

• Rezk, Charles W.
• Heller, Jeremiah Ben
• Stojanoska, Vesna
• Berwick-Evans, Daniel

• Algebraic Topology
• Primary Cohomology Operations In Algebraic Topology
• Dyer-lashof Operations

Statement dc:rights

• © 2025 Heyi Zhu All rights reserved.

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/130097

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F130097