Simple loop conjecture for limit groups
Group Theory
2013-09-10 v2
Abstract
There are noninjective maps from surface groups to limit groups that don't kill any simple closed curves. As a corollary, there are noninjective all-loxodromic representations of surface groups to SL(2,C) that don't kill any simple closed curves, answering a question of Minsky. There are also examples, for any k, of noninjective all-loxodromic representations of surface groups killing no curves with self intersection number at most k.
Keywords
Cite
@article{arxiv.1106.1350,
title = {Simple loop conjecture for limit groups},
author = {Larsen Louder},
journal= {arXiv preprint arXiv:1106.1350},
year = {2013}
}
Comments
13 pages, 2 figures, to appear in Israel Journal of Mathematics (accepted on Nov 5 2012)