Geodesic
Non-branching RCD(0,N) Geodesic Spaces with Small Linear Diameter Growth have Finitely Generated Fundamental Groups
Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 787-798

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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.
DOI : 10.4153/CMB-2015-052-4
Mots-clés : 53C23, 30L99, Milnor conjecture, non negative Ricci curvature, curvature dimension condition, finitely generated, fundamental group, infinitesimally Hilbertian 
Kitabeppu, Yu; Lakzian, Sajjad. Non-branching RCD(0,N) Geodesic Spaces with Small Linear Diameter Growth have Finitely Generated Fundamental Groups. Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 787-798. doi: 10.4153/CMB-2015-052-4
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     author = {Kitabeppu, Yu and Lakzian, Sajjad},
     title = {Non-branching {RCD(0,N)} {Geodesic} {Spaces} with {Small} {Linear} {Diameter} {Growth} have {Finitely} {Generated} {Fundamental} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {787--798},
     year = {2015},
     volume = {58},
     number = {4},
     doi = {10.4153/CMB-2015-052-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-052-4/}
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