Table 1.

Notation

1	$k_0,k_1,\cdots ,k_{m-1}$	Arcs of $\alpha$ in diagram $\alpha \cup \gamma$. See Sect. 2.2
2	$g_0,g_1,\cdots ,g_{s-1}$	Arcs of $\gamma$ in diagram $\alpha \cup \gamma$. See Sect. 2.2
3	$h_0,h_1,\cdots ,h_{t-1}$	Arcs of $\delta$ in diagram $\alpha \cup \gamma \cup \delta$. See Sect. 2.2
4	$ϵ(i)\in \{-1,1\}$	Local writhe number at the head of arc $k_i$
5	${ϵ}_{\gamma }(i)\in \{-1,1\}$	Local writhe number at the head of arc $g_i$
6	${ϵ}_{\delta }(i)\in \{-1,1\}$	Local writhe number at the head of arc $h_i$
7	f(i)	Subscript of overcrossing arc at head of arc $k_i$
8	$f_{\gamma }(i)$	Subscript of overcrossing arc at head of arc $g_i$
9	$f_{\delta }(i)$	Subscript of overcrossing arc at head of arc $h_i$
10	${ϵ}_1(i)\in \{-1,1\}$	Concerns 2-cells above inhomogeneous crossing of $\alpha$. See (1)
11	${ϵ}_2(i)\in \{-1,1\}$	Concerns 2-cells above inhomogeneous crossing of $\alpha$. See (2)
12	${ϵ}_3(i)\in \{-1,1\}$	Concerns 2-cells above a homogeneous crossing of $\alpha$. See (3)
13	${ϵ}_4^j(i)\in \{-1,0,1\}$	Concerns 2-cells above a crossing of $\alpha$ under $\gamma$. See (4)
14	${ϵ}_5^k(i)\in \{-1,0,1\}$	Concerns 2-cells above a crossing of $\delta$ under $\alpha$. See (9)
15	${ϵ}_6^{j,k}(i)\in \{0,1\}$	Concerns 2-cells above a crossing of $\delta$ under $\gamma$. See (10)