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Article Connectedness of the Cut System Complex on Nonorientable Surfaces(Univ Kragujevac, Fac Science, 2022) Ali, Fatema; Atalan, FeriheLet N be a compact, connected, nonorientable surface of genus g with n boundary components. In this note, we show that the cut system complex of N is connected for g < 4 and disconnected for g >= 4. We then define a related complex and show that it is connected for g >= 4.
