Sharp lower bounds and exact computations for two Kirby-Thompson invariants of knotted surfaces with bridge number ≤6.
Bounding the Kirby-Thompson invariant of spun knots
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abstract
A bridge trisection of a smooth surface in $S^4$ is a decomposition analogous to a bridge splitting of a link in $S^3$. 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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math.GT 1years
2022 1verdicts
UNVERDICTED 1representative citing papers
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Bounds for Kirby-Thompson invariants of knotted surfaces
Sharp lower bounds and exact computations for two Kirby-Thompson invariants of knotted surfaces with bridge number ≤6.