The bridge number of surface links and kei colorings

Kouki Sato; Kokoro Tanaka

doi:10.1112/blms.12654

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arXiv · 2004.07056

The bridge number of surface links and kei colorings

Kouki Sato·Kokoro Tanaka

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Abstract

Meier and Zupan introduced bridge trisections of surface links in $S^4$ as a 4-dimensional analogue to bridge decompositions of classical links, which gives a numerical invariant of surface links called the bridge number. We prove that there exist infinitely many surface knots with bridge number $n$ for any integer $n \geq 4$. To prove it, we use colorings of surface links by keis and give lower bounds for the bridge number of surface links.

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Kouki Sato, Kokoro Tanaka. 2020-04-15. The bridge number of surface links and kei colorings. https://doi.org/10.1112/blms.12654

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