148 \begin{equation*}

   148 \begin{equation*}

   149 \xymatrix{\bc_*^{\cC}(S^1) \ar[r]^{\iso}_{\text{qi}} & HC_*(\cC)}

   149 \xymatrix{\bc_*^{\cC}(S^1) \ar[r]^{\iso}_{\text{qi}} & HC_*(\cC)}

   150 \end{equation*}

   150 \end{equation*}

   151 \end{property}

   151 \end{property}

   152 

   152 

   154 \label{property:evaluation}%

   156 \label{property:evaluation}%

   156 \begin{equation*}

   158 \begin{equation*}

   157 \ev_X: \CD{X} \tensor \bc_*(X) \to \bc_*(X).

   159 \ev_X: \CD{X} \tensor \bc_*(X) \to \bc_*(X).

   158 \end{equation*}

   160 \end{equation*}

   159 (Here $\CD{X}$ is the singular chain complex of the space of diffeomorphisms of $X$, fixed on $\bdy X$.)

   161 (Here $\CD{X}$ is the singular chain complex of the space of diffeomorphisms of $X$, fixed on $\bdy X$.)

   160 

   162 

   168         \ar@/_4ex/[r]_{\ev_{X_1} \otimes \ev_{X_2}}  \ar[u]^{\gl^{\Diff}_Y \otimes \gl_Y}  &

   170         \ar@/_4ex/[r]_{\ev_{X_1} \otimes \ev_{X_2}}  \ar[u]^{\gl^{\Diff}_Y \otimes \gl_Y}  &

   169             \bc_*(X_1) \otimes \bc_*(X_2) \ar[u]_{\gl_Y}

   171             \bc_*(X_1) \otimes \bc_*(X_2) \ar[u]_{\gl_Y}

   170 }

   172 }

   171 \end{equation*}

   173 \end{equation*}

   172 \nn{should probably say something about associativity here (or not?)}

   174 \nn{should probably say something about associativity here (or not?)}

   173 \end{property}

   176 \end{property}

   174 

   177 

   175 

   178 

   176 \begin{property}[Gluing formula]

   179 \begin{property}[Gluing formula]

   177 \label{property:gluing}%

   180 \label{property:gluing}%