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

Published online by Cambridge University Press:  20 November 2018

Yu Kitabeppu  and
Sajjad Lakzian
Yu Kitabeppu
Affiliation:
Kyoto University e-mail: y.kitabeppu@gmail.com
Sajjad Lakzian
Affiliation:
Hausdorff Institute for Mathematics, Universität Bonn e-mail: lakzians@gmail.com
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Abstract

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In this paper, we generalize the finite generation result of Sormani to non-branching $RCD\left( 0,\,N \right)$ geodesic spaces (and in particular, Alexandrov spaces) with full supportmeasures. This is a special case of the Milnor’s Conjecture for complete non-compact $RCD\left( 0,\,N \right)$ spaces. One of the key tools we use is the Abresch–Gromoll type excess estimates for non-smooth spaces obtained by Gigli–Mosconi.

Keywords

53C2330L99Milnor conjecturenon negative Ricci curvaturecurvature dimension conditionfinitely generatedfundamental groupinfinitesimally Hilbertian
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 4 , 01 December 2015 , pp. 787 - 798
Copyright
Copyright © Canadian Mathematical Society 2015

References

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