A plat form presentation for surface-links

Jumpei Yasuda

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arXiv · 2105.08634

A plat form presentation for surface-links

Jumpei Yasuda

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Abstract

In this paper, we introduce a method, called a plat form, of describing a surface-link in the 4-space using a braided surface. We prove that every surface-link, which is not necessarily orientable, can be described in a plat form. The plat index is defined as a surface-link invariant, which is an analogy of the bridge index for a link in the 3-space. We classify surface-links with plat index $1$ and show some examples of surface-links in plat forms.

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Jumpei Yasuda. 2021-05-18. A plat form presentation for surface-links. https://arxiv.org/abs/2105.08634

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