equal
deleted
inserted
replaced
817 |
817 |
818 \begin{proof} |
818 \begin{proof} |
819 After a small perturbation, we may assume that $q$ is simultaneously transverse to all the splittings in $P$, and |
819 After a small perturbation, we may assume that $q$ is simultaneously transverse to all the splittings in $P$, and |
820 (by Axiom \ref{axiom:splittings}) that $c$ splits along $q$. |
820 (by Axiom \ref{axiom:splittings}) that $c$ splits along $q$. |
821 We can now choose, for each splitting $p$ in $P$, a common refinement $p'$ of $p$ and $q$. |
821 We can now choose, for each splitting $p$ in $P$, a common refinement $p'$ of $p$ and $q$. |
822 This constitutes the middle part of $\vcone(P)$. |
822 This constitutes the middle part ($P\times \{0\}$ above) of $\vcone(P)$. |
823 \end{proof} |
823 \end{proof} |
824 |
824 |
825 |
825 |
826 \noop{ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
826 \noop{ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
827 |
827 |