Yurttaş, S. Öykü2023-04-072023-04-072022Yurttaş, S.Ö. (2022). Curves on non-orientable surfaces and crosscap transpositions. Mathematics, 10(9), 1476.2227-7390https://www.mdpi.com/2227-7390/10/9/1476/pdf?version=1651213555&__cf_chl_tk=N2BKcIvPbCYIpws76iVyODMnUOAUJC51IExgnySlAQo-1680854043-0-gaNycGzNDyUhttps://hdl.handle.net/11468/11637Let N-g,N-n be a non-orientable surface of genus g with n punctures and one boundary component. In this paper, we describe multicurves in N-g,N-n making use of generalized Dynnikov coordinates, and give explicit formulae for the action of crosscap transpositions and their inverses on the set of multicurves in N-g,N-n in terms of generalized Dynnikov coordinates. This provides a way to solve on non-orientable surfaces various dynamical and combinatorial problems that arise in the study of mapping class groups and Thurston's theory of surface homeomorphisms, which were solved only on orientable surfaces before.eninfo:eu-repo/semantics/openAccessNon-orientable surfacesMulticurvesGeometric intersectionCrosscap transpositionsMapping class groupArticle109133WOS:0007946532000012-s2.0-8513262789210.3390/math10091476Q1Q1