Meridian and preferred longitude

Assume countable choice as in the chosen tubular-neighbourhood data. Let $K$ be a smooth oriented knot with chosen exterior $E_K$ and boundary torus $T_K=\mathrm{\partial }{E}_K$, and let $p:T_K\to K$ be the projection of the chosen normal-disk tube. Orient each normal disk so that its positive tangent direction followed by its oriented normal basis agrees with the orientation of $S^3$. A meridian $\mu$ is the oriented boundary of one such normal disk. A degree-one parallel curve is a simple closed curve $\lambda$ in $T_K$ for which $p{\mathrm{\mid }}_{\lambda }:\lambda \to K$ has degree $+1$. A preferred longitude is a degree-one parallel curve satisfying $i_{\ast }[\lambda ]=0$ in $H_1(E_K;\mathbb{Z})$, where $i:T_K\hookrightarrow E_K$ is inclusion. This is a condition on a curve; this definition alone asserts neither existence nor uniqueness. Reversing the orientation of $K$ reverses the orientations of both $\mu$ and any degree-one parallel curve. If a subgroup $P\le {\pi }_1(E_K,x)$ is specified using a path from $x$ to $T_K$, record it only up to replacing it by $gP{g}^{-1}$ for $g\in {\pi }_1(E_K,x)$.

Cattabriga and Francaviglia, §4.4

Calegari, §3.3