Bounds for Kirby-Thompson invariants of knotted surfaces

Román Aranda; Puttipong Pongtanapaisan; Cindy Zhang

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arXiv · 2206.02936

Bounds for Kirby-Thompson invariants of knotted surfaces

Román Aranda·Puttipong Pongtanapaisan·Cindy Zhang

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Abstract

We provide sharp lower bounds for two versions of the Kirby-Thompson invariants for knotted surfaces, one of which was originally defined by Blair, Campisi, Taylor, and Tomova. The second version introduced in this paper measures distances in the dual curve complex instead of the pants complex. We compute the exact values of both KT-invariants for infinitely many knotted surfaces with bridge number at most six.

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Román Aranda, Puttipong Pongtanapaisan, Cindy Zhang. 2022-06-06. Bounds for Kirby-Thompson invariants of knotted surfaces. https://arxiv.org/abs/2206.02936

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