Bridge Positions of Links That Cannot Be Monotonically Simplified

Puttipong Pongtanapaisan; Daniel Rodman

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arXiv · 2412.04621

Bridge Positions of Links That Cannot Be Monotonically Simplified

Puttipong Pongtanapaisan·Daniel Rodman

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Abstract

For any pair of integers $m$ and $n$ such that $3<m<n$, we provide an infinite family of links, where each link in the family has a locally minimal $n$-bridge position and a globally minimal $m$-bridge position. We accomplish this by applying the criterion of Takao et al. The $n$-bridge position is interesting because the corresponding bridge sphere is unperturbed, so it must be perturbed at least once before it can be de-perturbed to attain a globally minimal $m$-bridge sphere.

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BibTeX RIS

Puttipong Pongtanapaisan, Daniel Rodman. 2024-12-05. Bridge Positions of Links That Cannot Be Monotonically Simplified. https://arxiv.org/abs/2412.04621

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