A plat form presentation for surface-links
Jumpei Yasuda
TL;DR
This paper introduces a new method called a plat form for describing surface-links in 4-space using braided surfaces, establishing its universality and defining a new invariant called the plat index.
Contribution
It presents a novel plat form method for surface-links, proves its applicability to all surface-links, and introduces the plat index as a new invariant.
Findings
Every surface-link can be described in a plat form.
The plat index is a new invariant analogous to the bridge index.
Classification of surface-links with plat index 1 is provided.
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 and show some examples of surface-links in plat forms.
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Taxonomy
TopicsGeometric and Algebraic Topology · Computational Geometry and Mesh Generation · Advanced Numerical Analysis Techniques