T. Nagase

activity

20192021

collaborators

4 papers

math.CO2021

Properties of minimal charts and their applications VIII: charts of type $(7)$

Teruo Nagase, Akiko Shima

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 $(7)$ if there exists a label $m$ such that $w (Γ) = 7$ , $w(Γ_m\capΓ_{m+1})=…

math.GT2020

Properties of minimal charts and their applications VII: charts of type $(2, 3, 2)$

Teruo Nagase, Akiko Shima

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\capΓ_{m+…

math.GT2020

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

Teruo Nagase, Akiko Shima

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 $(m; 2, 3, 2)$ if $w (Γ) = 7$ , $w (Γ_{m} \cap Γ_{m + 1}) = 2$ , $w (Γ_{m + 1} \cap Γ_{m + 2}) = 3$ …

math.GT2019

Properties of minimal charts and their applications V: charts of type $(3, 2, 2)$

Teruo Nagase, Akiko Shima

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 $(3, 2, 2)$ if there exists a label $m$ such that $w (Γ) = 7$ , $w(Γ_m\capΓ_{m+…

Properties of minimal charts and their applications VIII: charts of type (7)

Properties of minimal charts and their applications VII: charts of type (2,3,2)

Properties of minimal charts and their applications VI: the graph Γm+1​ in a chart Γ of type (m;2,3,2)

Properties of minimal charts and their applications V: charts of type (3,2,2)

Properties of minimal charts and their applications VIII: charts of type $(7)$

Properties of minimal charts and their applications VII: charts of type $(2, 3, 2)$

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

Properties of minimal charts and their applications V: charts of type $(3, 2, 2)$