Crosscap number

In the mathematical field of knot theory, the crosscap number of a knot K is the minimum of

${\displaystyle C(K)\equiv 1-\chi (S),\,}$

taken over all compact, connected, non-orientable surfaces S bounding K; here ${\displaystyle \chi }$ is the Euler characteristic. The crosscap number of the unknot is zero, as the Euler characteristic of the disk is one.