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

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Published:2015-07-13
Printed: Dec 2015
• Yu Kitabeppu,
Kyoto University
• Sajjad Lakzian,
Hausdorff Institute for Mathematics, Universität Bonn
 Format: LaTeX MathJax PDF

## Abstract

In this paper, we generalize the finite generation result of Sormani to 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-smooth spaces obtained by Gigli-Mosconi.
 Keywords: Milnor conjecture, non negative Ricci curvature, curvature dimension condition, finitely generated, fundamental group, infinitesimally Hilbertian
 MSC Classifications: 53C23 - Global geometric and topological methods (a la Gromov); differential geometric analysis on metric spaces 30L99 - None of the above, but in this section

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