English

Complex Orientations are Partial Strictifications of the Unit

Algebraic Topology 2025-02-11 v4

Abstract

We give a higher-algebraic interpretation of complex orientations of ring spectra as "E2\mathbb{E}_2 strictifications" of the identity element. We show that higher strictifications do not exist for most ring spectra of interest in chromatic homotopy theory.

Keywords

Cite

@article{arxiv.2311.01663,
  title  = {Complex Orientations are Partial Strictifications of the Unit},
  author = {Doron Grossman-Naples},
  journal= {arXiv preprint arXiv:2311.01663},
  year   = {2025}
}

Comments

6 pages. Fixed a mistake where mapping spaces were taken in spaces rather than pointed spaces, cleaned up the exposition, and moved section boundaries around a bit for clarity

R2 v1 2026-06-28T13:10:14.977Z