596 \label{property:gluing-map}%

   596 \label{property:gluing-map}%

   597 %If $X_1$ and $X_2$ are $n$-manifolds, with $Y$ a codimension $0$-submanifold of $\bdy X_1$, and $Y^{\text{op}}$ a codimension $0$-submanifold of $\bdy X_2$, there is a chain map

   597 %If $X_1$ and $X_2$ are $n$-manifolds, with $Y$ a codimension $0$-submanifold of $\bdy X_1$, and $Y^{\text{op}}$ a codimension $0$-submanifold of $\bdy X_2$, there is a chain map

   598 %\begin{equation*}

   598 %\begin{equation*}

   599 %\gl_Y: \bc_*(X_1) \tensor \bc_*(X_2) \to \bc_*(X_1 \cup_Y X_2).

   599 %\gl_Y: \bc_*(X_1) \tensor \bc_*(X_2) \to \bc_*(X_1 \cup_Y X_2).

   600 %\end{equation*}

   600 %\end{equation*}

   602 a map

   602 a map

   603 \[

   603 \[

   604 	\bc_*(X) \to \bc_*(X \bigcup_{Y}\selfarrow),

   604 	\bc_*(X) \to \bc_*(X \bigcup_{Y}\selfarrow),

   605 \]

   605 \]

   606 natural with respect to homeomorphisms, and associative with respect to iterated gluings.

   606 natural with respect to homeomorphisms, and associative with respect to iterated gluings.

   693 Since the blob complex is functorial in the manifold $X$, this is equivalent to having chain maps

   693 Since the blob complex is functorial in the manifold $X$, this is equivalent to having chain maps

   694 $$ev_{X \to Y} : \CH{X \to Y} \tensor \bc_*(X) \to \bc_*(Y)$$

   694 $$ev_{X \to Y} : \CH{X \to Y} \tensor \bc_*(X) \to \bc_*(Y)$$

   695 for any homeomorphic pair $X$ and $Y$, 

   695 for any homeomorphic pair $X$ and $Y$, 

   696 satisfying corresponding conditions.

   696 satisfying corresponding conditions.

   697 

   697 

   699 

   699 

   700 \begin{thm}

   700 \begin{thm}

   701 \label{thm:blobs-ainfty}

   701 \label{thm:blobs-ainfty}

   702 Let $\cC$ be  a topological $n$-category.

   702 Let $\cC$ be  a topological $n$-category.

   703 Let $Y$ be an $n{-}k$-manifold. 

   703 Let $Y$ be an $n{-}k$-manifold.