On roots of Dehn twists

Naoyuki Monden

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arXiv · 0911.5079

On roots of Dehn twists

Naoyuki Monden

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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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Naoyuki Monden. 2009-12-17. On roots of Dehn twists. https://arxiv.org/abs/0911.5079

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