论文标题
紧凑型RCD（0，N）结构的模量空间
Moduli spaces of compact RCD(0,N)-structures
论文作者
论文摘要
本文的目的是设定基础，并证明有关在紧凑型拓扑空间上的合成意义上（通过最佳传输），具有非平滑度量度量结构的模量空间；更确切地说，我们研究了RCD（0，N）结构的模量空间。首先，我们将空间上RCD（0，N）结构的收敛性与相关的Lifts在通用覆盖物上的均衡收敛相关联。然后，我们构建了阿尔巴尼亚和灵魂地图，这反映了通用覆盖物上的结构如何分裂，我们证明了它们的连续性。最后，我们构建了具有非平凡有理同拷贝组的RCD（0，N）结构的模量空间的示例。
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.
