TL;DR
This paper explores mosaic diagrams for surface-links using marked graph diagrams, establishing bounds on mosaic numbers and applying these diagrams to enhance invariants for surface-links and classical knots.
Contribution
It introduces the concept of mosaic diagrams for surface-links and provides bounds on their mosaic numbers, also applying these diagrams to improve kei counting invariants.
Findings
Bounds on mosaic numbers for surface-links with ch-index up to 10
Enhanced kei counting invariant for unoriented surface-links
Application to classical knots and links
Abstract
We consider the notion of mosaic diagrams for surface-links using marked graph diagrams. We establish bounds, in some cases tight, on the mosaic numbers for the surface-links with ch-index up to 10. As an application, we use mosaic diagrams to enhance the kei counting invariant for unoriented surface-links as well as classical knots and links.
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Taxonomy
TopicsGeometric and Algebraic Topology · Topological and Geometric Data Analysis · Data Visualization and Analytics