= Zeeman theorem on twist-spun knots
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Let $K\subset S^3$ be a smooth <knot> and let $m\ne0$ be an <integer>. The exterior of its $m$-<twist-spun knot> in $S^4$ is a <fiber bundle> over a <circle>, with fiber the $|m|$-fold cyclic <branched covering> of $S^3$ along $K$ with an open <three-ball> removed. For the open complement, use the corresponding branched cover with a point removed. Its monodromy comes from the cyclic deck action.<Twisting spun knots by E. C. Zeeman>[Main theorem in Section 6; Section 1 distinguishes punctured and bounded-punctured fibers]{ref}
For $m=\pm1$, the branched cover is $S^3$, the compact fiber is a <three-ball>, and the resulting two-dimensional <surface knot> is unknotted. Zero-twist spinning is ordinary spinning and is excluded from this nonzero-twist fibration theorem; a zero-fold branched cover is not its fiber.<Twisting spun knots by E. C. Zeeman>[Corollary 2, page 487]{ref}
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