diff -r 082bfb8f6325 -r e3c5c55d901d text/basic_properties.tex --- a/text/basic_properties.tex Thu Dec 08 12:06:43 2011 -0800 +++ b/text/basic_properties.tex Thu Dec 08 15:57:34 2011 -0800 @@ -5,7 +5,7 @@ In this section we complete the proofs of Properties \ref{property:disjoint-union}--\ref{property:contractibility}. Throughout the paper, where possible, we prove results using Properties \ref{property:functoriality}--\ref{property:contractibility}, -rather than the actual definition of blob homology. +rather than the actual definition of the blob complex. This allows the possibility of future improvements on or alternatives to our definition. In fact, we hope that there may be a characterization of the blob complex in terms of Properties \ref{property:functoriality}--\ref{property:contractibility}, but at this point we are unaware of one. @@ -112,9 +112,9 @@ } 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. +``Natural" means natural with respect to the actions of homeomorphisms. In degree zero the map agrees with the gluing map coming from the underlying system of fields. \end{prop} This map is very far from being an isomorphism, even on homology. -We fix this deficit in \S\ref{sec:gluing} below. +We eliminate this deficit in \S\ref{sec:gluing} below.