Growth tightness and genericity for word metrics from injective spaces
Geometric Topology
2025-12-24 v4
Abstract
Mapping class groups are known to admit geometric (proper, cobounded) actions on injective spaces. Starting with such an action, and relying only on geometric arguments, we show that all finite generating sets resulting from taking large enough balls in the respective injective space yield word metrics where pseudo-Anosov maps are exponentially generic. We also show that growth tightness holds true for the Cayley graphs corresponding to these finite generating sets, providing a positive answer to a question by Arzhantseva, Cashen and Tao.
Keywords
Cite
@article{arxiv.2407.02378,
title = {Growth tightness and genericity for word metrics from injective spaces},
author = {Lihuang Ding and Dídac Martínez-Granado and Abdul Zalloum},
journal= {arXiv preprint arXiv:2407.02378},
year = {2025}
}
Comments
Final version incorporating all referee reports. Accepted for publication in Compositio Mathematica