Non-branching RCD$(0,N)$ Geodesic Spaces with Small Linear Diameter Growth have Finitely Generated Fundamental Groups

Canadian mathematical bulletin

Yu Kitabeppu¹  Sajjad Lakzian² 

[1] Kyoto University;Hausdorff Institute for Mathematics, Universität Bonn

关键词: Milnor conjecture;    non negative Ricci curvature;    curvature dimension condition;    finitely generated;    fundamental group;    infinitesimally Hilbertian;   

DOI  :  10.4153/CMB-2015-052-4

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this paper, we generalize the finite generation result of Sormanito non-branching $RCD(0,N)$ geodesic spaces (and in particular, Alexandrov spaces) with full support measures. This is a special case of the Milnor's Conjecture for complete non-compact $RCD(0,N)$ spaces. One of the key tools we use is the Abresch-Gromoll type excess estimates for non-smoothspaces obtained by Gigli-Mosconi.

【 授权许可】

Unknown