Calculus of Variations and Geometric Measure Theory

A. Mondino - D. Navarro

Moduli spaces of compact RCD(0,N)-structures

created by mondino on 01 Feb 2022
modified on 31 Oct 2022


Accepted Paper

Inserted: 1 feb 2022
Last Updated: 31 oct 2022

Journal: Math. Annalen
Year: 2022
Doi: 10.1007/s00208-022-02493-7


The goal of the paper is to set the foundations and prove some topological results about moduli spaces of non-smooth metric measure structures with non-negative Ricci curvature in a synthetic sense (via optimal transport) on a compact topological space; more precisely, we study moduli spaces of $RCD(0,N)$-structures. First, we relate the convergence of $RCD(0,N)$-structures on a space to the associated lifts' equivariant convergence on the universal cover. Then we construct the Albanese and soul maps, which reflect how structures on the universal cover split, and we prove their continuity. Finally, we construct examples of moduli spaces of $RCD(0,N)$-structures that have non-trivial rational homotopy groups.