o:1086520
COGROWTH FOR GROUP ACTIONS WITH STRONGLY CONTRACTING ELEMENTS
en
Let G be a group acting properly by isometries and with a strongly contracting element on a geodesic metric space. Let N be an infinite normal subgroup of G, and let δN and δG be the growth rates of N and G with respect to the pseudo-metric induced by the action. We prove that if G has purely exponential growth with respect to the pseudo-metric then δN /δG > 1/2. Our result applies to suitable actions of hyperbolic groups, right-angled Artin groups and other CAT(0) groups, mapping class groups, snowflake groups, small cancellation groups, etc. This extends Grigorchuk’s original result on free groups with respect to a word metrics and a recent result of Jaerisch, Matsuzaki, and Yabuki on groups acting on hyperbolic spaces to a much wider class of groups acting on spaces that are not necessarily hyperbolic.
Cogrowth, exponential growth, divergence type, contracting element, mapping class groups, right-angled Artin groups, snowflake groups, CAT(0) groups
1552099
10.1017/etds.2018.123
2020-06-16T08:14:25.375Z
44
yes
46
Christopher
Cashen
University of Vienna
0000-0002-6340-469X
application/pdf
188091
http://phaidra.univie.ac.at/o:1086520
no
yes
1
70
1552253
Ergodic Theory and Dynamical Systems
40
7
1738
1754
Cambridge University Press
2020-07-01