Factoring periodic maps into Dehn twists

2020/10/21 by Neeraj K. Dhanwani, Dhanwani, Neeraj K., Ajay K. Nair +3
Mathematics · Computer Science · #Geometric and Algebraic Topology #semigroups and automata theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2010.11161

Abstract

Let Mod(S_g) be the mapping class group of the closed orientable surface S_g of genus g ≥ 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 4g+2, for g≥ 2, whose product is pseudo-Anosov.

Related

• General primitivity in the mapping class group
• Liftability of periodic mapping classes under alternating covers
• Generating twist subgroup of mapping class group of non-orientable surface by involutions
• Generating the spin mapping class group by Dehn twists
• The mapping class group of a punctured surface is generated by three elements