On roots of Dehn twists

2009/11/26 by Naoyuki Monden, Monden, Naoyuki
Mathematics · #20F28 #57M99 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:20F28 #msc:57M99

paper · pdf · doi:10.48550/arxiv.0911.5079

12 pages, 6 figures

arxiv created 2009/12/17 · arxiv updated 2010/01/07

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.

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