$E_n$ ring spectra and Dyer-Lashof operations

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.

61 pages

References in corpus (2)

• Toda brackets and cup-one squares for ring spectra
• Calculating obstruction groups for E-infinity ring spectra