Abstract: We study the fundamental groups of open n-manifolds with nonnegative Ricci curvature. They are known to be virtually nilpotent in general. We introduce a quantity, escape rate, that measures how fast the representing geodesic loops escape from bounded balls. We show that if the escape rate is less than some positive constant epsilon(n), then the fundamental group is virtually abelian.
zoom link:
https://ucsb.zoom.us/j/9714609907
