Complex Orientations are Partial Strictifications of the Unit

2023/11/03 by Doron Grossman-Naples, Grossman-Naples, Doron
Mathematics · #55N22 (55P43) #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2311.01663

openalex publication_date 2023/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a higher-algebraic interpretation of complex orientations of ring spectra as "𝔼₂ strictifications" of the identity element. We show that higher strictifications do not exist for most ring spectra of interest in chromatic homotopy theory.

Related

• Tate-valued Characteristic Classes
• Strictly commutative complex orientation theory
• Units of ring spectra and Thom spectra
• Strict units of commutative ring spectra
• Adjoining roots in homotopy theory