Roots of crosscap slides and crosscap transpositions

Anna Parlak; Michał Stukow

doi:10.1007/s10998-017-0210-3

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arXiv · 1601.06096

Roots of crosscap slides and crosscap transpositions

Anna Parlak·Michał Stukow

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Abstract

Let $N_{g}$ denote a closed nonorientable surface of genus $g$. For $g \geq 2$ 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.

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Anna Parlak, Michał Stukow. 2017-01-03. Roots of crosscap slides and crosscap transpositions. https://doi.org/10.1007/s10998-017-0210-3

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