diff -r 270164061847 -r 6a3bc1c10586 text/basic_properties.tex --- a/text/basic_properties.tex Thu Jul 22 12:20:42 2010 -0600 +++ b/text/basic_properties.tex Thu Jul 22 13:22:34 2010 -0600 @@ -99,9 +99,8 @@ If $b = a$, then we can glue up blob diagrams on $X$ to get blob diagrams on $X\sgl$. This proves Property \ref{property:gluing-map}, which we restate here in more detail. -\todo{This needs more detail, because this is false without careful attention to non-manifold components, etc.} -\textbf{Property \ref{property:gluing-map}.}\emph{ +\begin{prop} \label{blob-gluing} There is a natural chain map \eq{ \gl: \bigoplus_a \bc_*(X; a, a, c) \to \bc_*(X\sgl; c\sgl). @@ -109,7 +108,7 @@ The sum is over all fields $a$ on $Y$ compatible at their ($n{-}2$-dimensional) boundaries with $c$. ``Natural" means natural with respect to the actions of diffeomorphisms. -} +\end{prop} This map is very far from being an isomorphism, even on homology. We fix this deficit in \S\ref{sec:gluing} below.