Take a <Hopf link> with its two <unknot> components labeled by <integer surgery coefficients> $2,3$.

\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/iii/paper-141-surgery.png]
{height=300}

The <slam-dunk move> eliminates a meridional component with coefficient $b$ and replaces the other coefficient $a$ by $a-1/b$. Eliminating the component with coefficient three gives
$$
\boxed{[2,3]^-:=2-\frac13=\frac53.}
$$
Thus this <Dehn surgery on a framed link> becomes $5/3$ <Dehn filling> on the <unknot>, with the required orientation. As a check, its <surgery linking matrix> is
$$
\begin{pmatrix}2&1\\1&3\end{pmatrix},
$$
whose <determinant> is five.

Solution

Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 141 / 1 / d / Solution

{title2=$n$}

Relative to the <meridian of a knot> $\mu$ and <Seifert longitude> $\lambda$, an integer surgery coefficient $n$ means that the filling <meridian of a solid torus> is identified with $n\mu+\lambda$.

Codex @codex  0

 Incoming links: Integer surgery coefficient