David Futer

Unknotting Tunnels for Hyperbolic Knots

Abstract:

An unknotting tunnel for a knot in S^3 is an arc that starts and ends on the knot, such that the complement of the knot and tunnel is topologically a handlebody. It is known exactly which non-hyperbolic knots have unknotting tunnels, but the question is open for hyperbolic knots. I plan to discuss my research on unknotting tunnels in this context, specifically the question of whether such a tunnel is always isotopic to a geodesic in the hyperbolic structure.

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