$E_n$ 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.

arXiv comment61 pages

References in corpus (16)

• Algebras and modules in monoidal model categories
• Diagram spaces and symmetric spectra
• Homology and Cohomology of E-infinity Ring Spectra
• Model Structures on Commutative Monoids in General Model Categories
• Topological Hochschild homology and cohomology of A_\infty ring spectra
• The Picard group of topological modular forms via descent theory
• Parametrized spectra, multiplicative Thom spectra, and the twisted Umkehr map
• Rigidification of algebras over multi-sorted theories
• The Multiplication on BP
• Bar constructions and Quillen homology of modules over operads
• For Complex Orientations Preserving Power Operations, p-typicality is Atypical
• The smash product for derived categories in stable homotopy theory
• Power operations in the Kunneth spectral sequence and commutative HFp-algebras
• Toda brackets and cup-one squares for ring spectra
• On the secondary Steenrod algebra
• Calculating obstruction groups for E-infinity ring spectra