Stratified Noncommutative Geometry

David Ayala, Montana State University, Bozeman, Montana, Aaron Mazel-Gee, California Institute of Technology, Palo Alto, California, and Nick Rozenblyum, University of Chicago, Illinois.

1. Introduction 2. Detailed overview and fundamental examples 3. Stratified noncommutative geometry 4. Fundamental operations 5. The $\mathcal {O}$-monoidal reconstruction theorem 6. The geometric stratification of genuine $G$-spectra 7. The metacosm reconstruction theorem 8. Variations on the metacosm reconstruction theorem A. Actions and limits, strict and lax B. Some $(\infty ,2)$-category theory