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Factoring periodic maps into Dehn twists

Affiliation:	1. Department of Mathematics, Indian Institute of Science Education and Research Bhopal, Bhopal Bypass Road, Bhauri, Bhopal 462 066, Madhya Pradesh, India;2. Department of Mathematics, Indian Institute of Science, Bangalore - 560 012, Karnataka, India;1. Sistiana Mare 56, 34011 Trieste, Italy;2. Departamento de Matemáticas, Universidad de La Serena, Cisternas 1200, 1700000 La Serena, Chile;3. IMUV, Universidad de Valparaíso, Gran Bretaña 1111, 2340000 Valparaíso, Chile;1. University of Missouri-Columbia, Mathematics Department, Columbia, MO, USA;2. College of the Ozarks, Mathematics Department, Point Lookout, MO, USA

Abstract:	Let $Mod (S_{g})$ be the mapping class group of the closed orientable surface $S_{g}$ of genus $g \geq 1$ . In this paper, we develop various methods for factoring periodic mapping classes into Dehn twists, up to conjugacy. As applications, we develop methods for factoring certain roots of Dehn twists as words in Dehn twists. We will also show the existence of conjugates of periodic maps of order 4g and $4 g + 2$ , for $g \geq 2$ , whose product is pseudo-Anosov.

Keywords:	Surface Mapping class Periodic maps Dehn twists
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