Connectedness of the Cut System Complex on Nonorientable Surfaces

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DOI: 10.46793/KgJMat2201.021A


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.


A nonorientable surface, cut system complex.


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