A categorical approach to interactions between mod 2 power operations
Zhu, Heyi
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/130097
Description
Title
A categorical approach to interactions between mod 2 power operations
Author(s)
Zhu, Heyi
Issue Date
2025-07-16
Director of Research (if dissertation) or Advisor (if thesis)
Rezk, Charles W.
Doctoral Committee Chair(s)
Heller, Jeremiah Ben
Committee Member(s)
Stojanoska, Vesna
Berwick-Evans, Daniel
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Algebraic Topology
Primary Cohomology Operations In Algebraic Topology
Dyer-lashof Operations
Language
eng
Abstract
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.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
