Kirby-Thompson invariants of distant sums of standard surfaces

Minami Taniguchi

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arXiv · 2405.06976

Kirby-Thompson invariants of distant sums of standard surfaces

Minami Taniguchi

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Abstract

Blair, Campisi, Taylor, and Tomova defined the L-invariant L(F) of a knotted surface F, using pants complexes of trisection surfaces of bridge trisections of F. After that, Aranda, Pongtanapaisan, and Zhang introduced the L*-invariant L*(F) using dual curve complexes instead of pants complexes. In this paper, we determine both of L-invariant and L*-invariant of any finite distant sum of standard surfaces, and this is the first example of knotted surfaces whose bridge numbers and these invariants can be arbitrary large.

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Minami Taniguchi. 2024-05-11. Kirby-Thompson invariants of distant sums of standard surfaces. https://arxiv.org/abs/2405.06976

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