CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

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

  Published:2015-07-13
 Printed: Dec 2015
  • Yu Kitabeppu,
    Kyoto University
  • Sajjad Lakzian,
    Hausdorff Institute for Mathematics, Universit├Ąt 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 Milnor conjecture, non negative Ricci curvature, curvature dimension condition, finitely generated, fundamental group, infinitesimally Hilbertian
MSC Classifications: 53C23, 30L99 show english descriptions Global geometric and topological methods (a la Gromov); differential geometric analysis on metric spaces
None of the above, but in this section
53C23 - Global geometric and topological methods (a la Gromov); differential geometric analysis on metric spaces
30L99 - None of the above, but in this section
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/