## Seminar October 4: Dave Futer

On October 4, the geometry-topology seminar continues with an internal speaker, Dave Futer.

Title: Detecting fiber surfaces

Abstract: For a knot diagram $D(K)$, a state surface is a certain surface with boundary along $K$, algorithmically constructed from $D(K)$ by making a binary choice at each crossing. This construction generalizes Seifert’s algorithm for constructing an orientable surface with boundary $K$. I will describe this construction and discuss a simple diagrammatic criterion that characterizes when one of these state surfaces is a fiber in the knot complement $S^3 \setminus K$.

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