E_n ring spectra and Dyer-Lashof operations

2020/02/10 by Lawson, Tyler
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.03889

Abstract

This is an expository article about power operations and their connection with the study of highly structured ring spectra. In particular, we discuss Dyer-Lashof operations and their evolving role in the study of iterated loop spaces, E_n-algebras, and E_n-ring spectra. We will make use of these operations to show that structured ring spectra are heavily constrained. We also discuss some ongoing directions for study. This is a preliminary version of a chapter written for the Handbook of Homotopy Theory.

Related

• Power operations and coactions in highly commutative homology theories
• Stable power operations
• Higher homotopy excision and Blakers-Massey theorems for structured ring spectra
• What precisely are E_∞ ring spaces and E_∞ ring spectra?
• The construction of E_∞ ring spaces from bipermutative categories