Assumption 8.2 Suppose that each fibre $N_{a,b,c}$ of $f$ may be written

	$\displaystyle N_{a,b,c}=\Bigl\{($	$\displaystyle z_{1},z_{2},z_{3}+2\pi\mathbin{\mathbb{Z}})\in U:\mathop{\rm Re}(z_{1}z_{2})=u_{a,b}\bigl(\mathop{\rm Re}(z_{3})+2\pi\mathbin{\mathbb{Z}},\mathop{\rm Im}(z_{1}z_{2})\bigr),$
		$\displaystyle\mathop{\rm Im}(z_{3})=v_{a,b}\bigl(\mathop{\rm Re}(z_{3})+2\pi\mathbin{\mathbb{Z}},\mathop{\rm Im}(z_{1}z_{2})\bigr)+c,\;\>|z_{1}|^{2}-|z_{2}|^{2}=a\Bigr\},$

where $u_{a,b},v_{a,b}$ are functions $(\mathbin{\mathbb{R}}/2\pi\mathbin{\mathbb{Z}})\times[-\pi,\pi]\rightarrow\mathbin{\mathbb{R}}$. Suppose also that $u_{a,b}$ and $v_{a,b}$ satisfy parts (i)–(vi) of Assumption 7.1.