Roots of crosscap slides and crosscap transpositions

Abstract

Let $N_g$ denote a closed nonorientable surface of genus $g$. For $g\ge 2$ the mapping class group $\mathcal{M}(N_g)$ is generated by Dehn twists and one crosscap slide ($Y$-homeomorphism) or by Dehn twists and a crosscap transposition. Margalit and Schleimer observed that Dehn twists have nontrivial roots. We give necessary and sufficient conditions for the existence of a root of a crosscap slide and a crosscap transposition.

6 pages, 2 figures; revised version

Cited by in corpus (1)

• Roots of Dehn twists on nonorientable surfaces