Curves on non--orientable surfaces and crosscap transpositions

S. Öykü Yurttaş

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arXiv · 1909.12190

Curves on non--orientable surfaces and crosscap transpositions

S. Öykü Yurttaş

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Abstract

Let $N_{g,n}$ be an $n$--punctured non--orientable surface of genus $g$ with one boundary component. For $g\geq 2$ one of the generators of the mapping class group of $N_{g,n}$ is a crosscap transposition. We give explicit formulae for the action of crosscap transpositions and their inverses on the set of multicurves in $N_{g,n}$ in terms of generalized Dynnikov coordinates.

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S. Öykü Yurttaş. 2019-09-26. Curves on non--orientable surfaces and crosscap transpositions. https://arxiv.org/abs/1909.12190

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