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

Curves on non--orientable surfaces and crosscap transpositions