The primitivity index function for a free group, and untangling closed curves on hyperbolic surfaces. With an appendix by Khalid Bou-Rabee
Group Theory
2017-09-08 v4 Differential Geometry
Geometric Topology
Abstract
Motivated by the results of Scott and Patel about "untangling" closed geodesics in finite covers of hyperbolic surfaces, we introduce and study primitivity, simplicity and non-filling index functions for finitely generated free groups. We obtain lower bounds for these functions and relate these free group results back to the setting of hyperbolic surfaces. An appendix by Khalid Bou-Rabee connects the primitivity index function to the residual finiteness growth function for .
Keywords
Cite
@article{arxiv.1411.5523,
title = {The primitivity index function for a free group, and untangling closed curves on hyperbolic surfaces. With an appendix by Khalid Bou-Rabee},
author = {Neha Gupta and Ilya Kapovich},
journal= {arXiv preprint arXiv:1411.5523},
year = {2017}
}
Comments
Final version. To appear in Math. Proc. Cambridge Phil. Soc