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arXiv · 1405.0897

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

Yu Kitabeppu·Sajjad Lakzian
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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-Mosconii.

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Yu Kitabeppu, Sajjad Lakzian. 2014-05-05. Non-branching RCD(0,N) Geodesic Spaces with Small Linear Diameter Growth Have Finitely Generated Fundamental Groups. https://arxiv.org/abs/1405.0897

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