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Bounds for Kirby–Thompson invariants of knotted surfaces
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Journal Article
Bounds for Kirby–Thompson invariants of knotted surfaces
2023
Overview
Blair, Campisi, Taylor, and Tomova introduced a non-negative integer-valued invariant
L
(
S
)
of a smooth surface
S
in the 4-sphere. In this paper, we extend previous work done by the authors with Scott Taylor to compute the invariant
L
(
S
)
of a knotted surface in 4-space. We further explore the combinatorics of pants decompositions to give sharp bounds for the
L
-invariant of large families of bridge trisections. As an application, we show that surfaces with
L
(
S
)
≤
2
must be unknotted.
Publisher
Springer Netherlands
