• Corpus ID: 214667334

Properties of minimal charts and their applications VI: the graph $\Gamma_{m+1}$ in a chart $\Gamma$ of type $(m;2,3,2)$

@article{Nagase2020PropertiesOM,
  title={Properties of minimal charts and their applications VI: the graph \$\Gamma\_\{m+1\}\$ in a chart \$\Gamma\$ of type \$(m;2,3,2)\$},
  author={Teruo Nagase and Akiko Shima},
  journal={arXiv: Geometric Topology},
  year={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 $w(\Gamma)=7$, $w(\Gamma_m\cap\Gamma_{m+1})=2$, $w(\Gamma_{m+1}\cap\Gamma_{m+2})=3$, and $w(\Gamma_{m+2}\cap\Gamma_{m+3})=2$ where $w(G)$ is the number of white vertices in $G$. In this paper, we prove that if there is a minimal chart $\Gamma$ of type $(m;2,3,2)$, then each of $\Gamma_{m+1}$ and $\Gamma_{m+2}$ contains one of three kinds of graphs. In the next… 

References

SHOWING 1-10 OF 18 REFERENCES
Properties of minimal charts and their applications VII: Charts of type (2,3,2)
Abstract Let Γ be a chart, and we denote by Γ m the union of all the edges of label m. A chart Γ is of type ( 2 , 3 , 2 ) if there exists a label m such that w ( Γ ) = 7 , w ( Γ m ∩ Γ m + 1 ) = 2 , w
Properties of minimal charts and their applications V: Charts of type (3,2,2)
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 $(3,2,2)$ if there exists a label $m$ such that $w(\Gamma)=7$,
The structure of a minimal n-chart with two crossings I: Complementary domains of Γ1 ∪ Γn−1
This is the first step of the two steps to enumerate the minimal charts with two crossings. For a label [Formula: see text] of a chart [Formula: see text] we denote by [Formula: see text] the union
Minimal charts of type
  • Proc. Sch. Sci. TOKAI UNIV
  • 2017
Properties of Minimal Charts and Their Applications IV: Loops
We investigate minimal charts with loops, a simple closed curve consisting of edges of label m containing exactly one white vertex. We shall show that there does not exist any loop in a minimal chart
Minimal charts of type (3,3)
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
THE CLOSURES OF SURFACE BRAIDS OBTAINED FROM MINIMAL n-CHARTS WITH FOUR WHITE VERTICES
In this paper, we investigate surface braids obtained from minimal charts with exactly four white vertices.
MINIMAL n-CHARTS WITH FOUR WHITE VERTICES
Properties of minimal charts and their applications II
We investigate minimal charts with loops, a simple closed curve consisting of edges of label $m$ containing exactly one white vertex. We shall show that there does not exist any loop in a minimal
Properties of minimal charts and their applications I
We study surface braids using the charts with minimal complexity. We introduce several terminology to describe minimal charts and investigate properties of minimal charts. We shall show that in a
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