Geodesic
Connectedness of the Cut System Complex on Nonorientable Surfaces
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 1, p. 21

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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 $g \geq 4$. We then define a related complex and show that it is connected for $g \geq 4$.
Classification : 57N05, 57M99, 05C40
Keywords: a nonorientable surface, cut system complex 
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     author = {Fatema Ali and Ferihe Atalan},
     title = {Connectedness of the {Cut} {System} {Complex} on {Nonorientable} {Surfaces}},
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Fatema Ali; Ferihe Atalan. Connectedness of the Cut System Complex on Nonorientable Surfaces. Kragujevac Journal of Mathematics, Tome 46 (2022) no. 1, p. 21 . http://geodesic.mathdoc.fr/item/KJM_2022_46_1_a1/