# Nilpotency Conjecture, a Geometric Approach to Milnor's Problem on Group Growth

From the geometric viewpoint, Nilpotency Conjecture is a natural extension of earlier known results and conjectures on the fundamental group of manifolds under lower curvature bounds. We will verify the Nilpotency Conjecture in some cases, and we will verify the vanishing gap phenomena for more cases i.e., if $h(M)<\epsilon(n,d)$, then $h(M)=0$.  The gap phenomena was raised to the author by S. Honda in 2016.

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