Crosscap number of a knot
\textit{B. E. Clark} [Int. J. Math. Math. Sci. 1, 113-124 (1978; Zbl 0386.57003)] defined the crosscap number of a knot to be the minimum number of the first Betti numbers of non-orientable surfaces bounding it. In this paper, we investigate the crosscap numbers of knots. We show that the crosscap number of \(7_4\) is equal to 3. This gives an affirmative answer to a question given by Clark. In general, the crosscap number is not additive under the connected sum. We give a necessary and sufficient condition for the crosscap number to be additive under the connected sum.
scientific article; zbMATH DE number 912144