• 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}
}
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 $(m;2,3,2)$
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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