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

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- Solution c

Solution

Choose Seifert longitudes

λ_{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} # K_{2}

, and therefore

λ_{K_{1} # K_{2}} = λ_{1} # λ_{2} .

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