diff -r ef8fac44a8aa -r 6e23226d1cca text/basic_properties.tex --- a/text/basic_properties.tex Mon May 31 23:42:37 2010 -0700 +++ b/text/basic_properties.tex Tue Jun 01 11:34:03 2010 -0700 @@ -3,7 +3,7 @@ \section{Basic properties of the blob complex} \label{sec:basic-properties} -In this section we complete the proofs of Properties 1-4. Throughout the paper, where possible, we prove results using Properties 1-4, rather than the actual definition of blob homology. This allows the possibility of future improvements to or alternatives on our definition. In fact, we hope that there may be a characterisation of blob homology in terms of Properties 1-4, but at this point we are unaware of one. +In this section we complete the proofs of Properties 1-5. Throughout the paper, where possible, we prove results using Properties 1-5, rather than the actual definition of blob homology. This allows the possibility of future improvements to or alternatives on our definition. In fact, we hope that there may be a characterisation of blob homology in terms of Properties 1-5, but at this point we are unaware of one. Recall Property \ref{property:disjoint-union}, that there is a natural isomorphism $\bc_*(X \du Y) \cong \bc_*(X) \otimes \bc_*(Y)$. @@ -106,3 +106,5 @@ This map is very far from being an isomorphism, even on homology. We fix this deficit in Section \ref{sec:gluing} below. + +As we pointed out earlier, Property \ref{property:skein-modules} is immediate from the definitions.