Bounding the Kirby-Thompson invariant of spun knots
Abstract
A bridge trisection of a smooth surface in S4 is a decomposition analogous to a bridge splitting of a link in S3. The Kirby-Thompson invariant of a bridge trisection measures its complexity in terms of distances between disc sets in the pants complex of the trisection surface. We give the first significant bounds for the Kirby-Thompson invariant of spun knots. In particular, we show that the Kirby-Thompson invariant of the spun trefoil is 15.
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