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On roots of Dehn twists. (English) Zbl 1302.57056
Summary: D. Margalit and S. Schleimer [Geom. Topol. 13, No. 3, 1495–1497 (2009; Zbl 1203.57007)] discovered a nontrivial root of the Dehn twist about a nonseparating curve on a closed oriented connected surface. We give a complete set of conjugacy invariants for such a root by using a classification theorem of Y. Matsumoto and J. M. Montesinos-Amilibia [Pseudo-periodic maps and degeneration of Riemann surfaces. Lecture Notes in Mathematics 2030. Berlin: Springer (2011; Zbl 1239.57001), Bull. Am. Math. Soc., New Ser. 30, No.1, 70–75 (1994; Zbl 0797.30036)] for pseudo-periodic maps of negative twists. As an application, we determine the range of degree for roots of a Dehn twist.

MSC:
57M99 General low-dimensional topology
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