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

Kitabeppu, Yu ; Lakzian, Sajjad

Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 787-798

Résumé

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.

Détail

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

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