Choose <Seifert longitude>[Seifert longitudes] $\lambda_i$ disjoint from the small arcs removed in forming the <connected sum of knots>. Join the two resulting longitude arcs through the same connecting tube used for the knots. Their oriented band sum is a zero-linking parallel of $K_1\mathbin\#K_2$, and therefore
$$
\boxed{\lambda_{K_1\#K_2}=\lambda_1\mathbin\#\lambda_2.}
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 141 / 3 / c / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-141/3/c/solution