On the universal cover and the fundamental group of an \(\mathsf{RCD}^\ast(K,N)\)-space

DOI10.1515/crelle-2016-0068zbMath1422.53033arXiv1605.02854OpenAlexW3100220102MaRDI QIDQ2317010

Andrea Mondino, Guofang Wei

Publication date: 7 August 2019

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.02854

zbMATH Keywords

fundamental groupuniversal coversRicci limit spaces

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (13)

Maximal volume entropy rigidity for RCD∗(−(N−1),N) spaces ⋮ An upper bound on the revised first Betti number and a torus stability result for \textsf{RCD} spaces ⋮ Quantitative maximal volume entropy rigidity on Alexandrov spaces ⋮ Maximal first Betti number rigidity of noncompact RCD(0,𝑁) spaces ⋮ Singular Weyl’s law with Ricci curvature bounded below ⋮ A note on the topological stability theorem from RCD spaces to Riemannian manifolds ⋮ Moduli spaces of compact \(\mathrm{RCD}(0,N)\)-structures ⋮ Quantitative rigidity of almost maximal volume entropy for both \(\mathsf{RCD}^\ast\) spaces and integral Ricci curvature bound ⋮ On fundamental groups of RCD spaces ⋮ Topological and Geometric Rigidity for Spaces with Curvature Bounded Below ⋮ Torus stability under Kato bounds on the Ricci curvature ⋮ \(RCD^*(K,N)\) spaces are semi-locally simply connected ⋮ Isometric immersions of \(\mathrm{RCD}(K, N)\) spaces via heat kernels

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