Year: 2025
Type: preprint
Abstract: Niebrzydowski introduced a theory of region colorings for surface links. In this paper, we translate the coloring invariant to the context of triplane diagrams and movies of knots. We provide inequalities between the number of region colorings and topological quantities of $F$, such as the number of saddles in a movie and the bridge index of a triplane diagram of $F$. As an application, we show that Yoshikawa's 2-knots $9_1$ and $10_2$ are non-invertible; that is $F\not=-F$.
Source: arXiv (Cornell University)
Authors: Aranda, Román, Crawford, Noah, Maas, Andrew, Marienau, Nicole, Pearce, Erica, Sarreal, Renzo, Schutte, Savannah, Sterns, Ransom, Woods, Eric
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979297225
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