On roots of Dehn twists
Geometric Topology
2009-12-17 v2 Group Theory
Abstract
Margalit and Schleimer constructed nontrivial roots of the Dehn twist about a nonseparating curve. We prove that the conjugacy classes of roots of the Dehn twist about a nonseparating curve correspond to the conjugacy classes of periodic maps with certain conditions. Futhermore, we give data set which determine the conjugacy class of a root. As a consequence, we can find the minimum degree and the maximum degree, and show that the degree must be odd. Also, we give Dehn twist expression of the root of degree 3.
Cite
@article{arxiv.0911.5079,
title = {On roots of Dehn twists},
author = {Naoyuki Monden},
journal= {arXiv preprint arXiv:0911.5079},
year = {2009}
}
Comments
12 pages, 6 figures