diff -r 62a402dd3e6e -r b138ee4a5938 text/basic_properties.tex --- a/text/basic_properties.tex Thu Sep 23 18:10:35 2010 -0700 +++ b/text/basic_properties.tex Fri Sep 24 15:32:55 2010 -0700 @@ -3,12 +3,12 @@ \subsection{Basic properties} \label{sec:basic-properties} -In this section we complete the proofs of Properties 2-4. \nn{fix these numbers} -Throughout the paper, where possible, we prove results using Properties 1-4, +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. 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 1-4, but at this point we are unaware of one. +terms of Properties \ref{property:functoriality}--\ref{property:contractibility}, but at this point we are unaware of one. Recall Property \ref{property:disjoint-union}, that there is a natural isomorphism $\bc_*(X \du Y) \cong \bc_*(X) \otimes \bc_*(Y)$.