Twist-spun knot (${\mathrm{Tw}}_m(K)$)

An $m$-twist spin removes a trivial arc from a knot and spins the resulting knotted arc around the boundary of a three-ball in $S^4$, inserting $m$ full twists during one revolution.

Zeeman's theorem says that the complement of an $m$-twist spin fibers over the circle with fiber the punctured $m$-fold cyclic branched cover of the original knot. In particular, the $1$- and $-1$-twist spins are unknotted.