2026/07/20 by Koji Fujiwara, Sang-hyun Kim, Ryokichi Tanaka
#math.GR
We introduce the notion of a Magnus marking for a finite generating set of a group and prove a certain expansion property. Using this property, we determine the second and third smallest growth rates of the rank-d free group for d≥ 2. We also give a new lower bound for the smallest growth rate of the genus-g surface group for g≥ 2, as well as a lower bound for the growth rate associated with a one-relator presentation.