In the mathematical field of knot theory, the crosscap number of a knot K is the minimum of C ( K ) ≡ 1 − χ ( S ) , {\displaystyle C(K)\equiv 1-\chi (S),\,} taken over all compact, connected, non-orientable surfaces S bounding K; here χ {\displaystyle \chi } is the Euler characteristic. The crosscap number of the unknot is zero, as the Euler characteristic of the disk is one.
In the mathematical field of knot theory, the crosscap number of a knot K is the minimum of C ( K ) ≡ 1 − χ ( S ) , {\displaystyle C(K)\equiv 1-\chi (S),\,} taken over all compact, connected, non-orientable surfaces S bounding K; here χ {\displaystyle \chi } is the Euler characteristic. The crosscap number of the unknot is zero, as the Euler characteristic of the disk is one.
Source: Wikipedia "Crosscap number" · CC BY-SA 4.0
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