CONNECTEDNESS OF THE CUT SYSTEM COMPLEX ON NONORIENTABLE SURFACES
Fatema Ali, Ferihe Atalan · Kragujevac Journal of Mathematics · 2022
Let 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.