• Corpus ID: 119670065

Minimal charts of type (3,3)

```@article{Nagase2016MinimalCO,
title={Minimal charts of type (3,3)},
author={Teruo Nagase and Akiko Shima},
journal={arXiv: Geometric Topology},
year={2016}
}```
• Published 27 September 2016
• Mathematics
• arXiv: Geometric Topology
Let \$\Gamma\$ be a chart. For each label \$m\$, we denote by \$\Gamma_m\$ the "subgraph" of \$\Gamma\$ consisting of all the edges of label \$m\$ and their vertices. Let \$\Gamma\$ be a minimal chart of type \$(m;3,3)\$. That is, a minimal chart \$\Gamma\$ has six white vertices, and both of \$\Gamma_m\cap\Gamma_{m+1}\$ and \$\Gamma_{m+1}\cap\Gamma_{m+2}\$ consist of three white vertices. Then \$\Gamma\$ is C-move equivalent to a minimal chart containing a "subchart" representing a 2-twist spun trefoil or its…
2 Citations
Properties of minimal charts and their applications VI: the graph \$\Gamma_{m+1}\$ in a chart \$\Gamma\$ of type \$(m;2,3,2)\$
• Mathematics
• 2020
Let \$\Gamma\$ be a chart, and we denote by \$\Gamma_m\$ the union of all the edges of label \$m\$. A chart \$\Gamma\$ is of type \$(m;2,3,2)\$ if \$w(\Gamma)=7\$, \$w(\Gamma_m\cap\Gamma_{m+1})=2\$,

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