Abstract: The theory of Normal Surfaces was developed by Kneser and expanded by Haken to find properly embedded essential surfaces triangulations of compact 3-manifolds. For ideal triangulations of cusped finite-volume hyperbolic 3-manifolds, Walsh showed if the ideal triangulation has essential edges, any incompressible surface $S$ can be realized as a spun-normal surface, provided $S$ is not a virtual fiber. One comes to the natural question posed directly by Cooper, Tillmann, and Worden:
"For a fibered knot complement or fibered once-cusped 3-manifold $M$, is there always some ideal triangulation of $M$ such that the fiber is realized as an embedded spun-normal surface?" Using the techniques of crushing and inflating ideal triangulations developed by Jaco and Rubinstein, we will answer this question by giving an algorithm to construct for a fibered knot complement an ideal triangulation, $\mathcal T^*$, in which a fiber of the bundle structure spun-normalizes. The algorithm presented will also identify the fiber within a finite set of normal surface solutions of $\mathcal T^*$.
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