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# Crosscap number

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

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

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.

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• Concordance Crosscap Number of a Knot (part 1/3)
• Crosscap Sliceform
• Energy of a knot part 1/4

## Examples

The formula for the knot sum is

${\displaystyle C(k_{1})+C(k_{2})-1\leq C(k_{1}\#k_{2})\leq C(k_{1})+C(k_{2}).\,}$