2087 manifold.)

  2087 manifold.)

  2088 We have $\bd X_i = Y_i \cup \ol{Y}_i \cup (D\times I)$

  2088 We have $\bd X_i = Y_i \cup \ol{Y}_i \cup (D\times I)$

  2089 (see Figure \ref{jun23a}).

  2089 (see Figure \ref{jun23a}).

  2090 \begin{figure}[t]

  2090 \begin{figure}[t]

  2091 \begin{equation*}

  2091 \begin{equation*}

  2093 \end{equation*}

  2093 \end{equation*}

  2094 \caption{$Y\times I$ sliced open}

  2094 \caption{$Y\times I$ sliced open}

  2095 \label{jun23a}

  2095 \label{jun23a}

  2096 \end{figure}

  2096 \end{figure}

  2097 Given $a_i\in \cS(Y_i)$, $b_i\in \cS(\ol{Y}_i)$ and $v\in\cS(D\times I)$

  2097 Given $a_i\in \cS(Y_i)$, $b_i\in \cS(\ol{Y}_i)$ and $v\in\cS(D\times I)$