English

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.

Keywords

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