# HG changeset patch # User Scott Morrison # Date 1275610777 25200 # Node ID 160ca7078ae930dd16a68d9511e0806116832623 # Parent eb03c4a92f98e20cf0aa416444b596cd757685c0 fixing some inconsistencies in where the easy basic properties are treated diff -r eb03c4a92f98 -r 160ca7078ae9 text/basic_properties.tex --- a/text/basic_properties.tex Thu Jun 03 12:33:47 2010 -0700 +++ b/text/basic_properties.tex Thu Jun 03 17:19:37 2010 -0700 @@ -106,5 +106,3 @@ 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. diff -r eb03c4a92f98 -r 160ca7078ae9 text/blobdef.tex --- a/text/blobdef.tex Thu Jun 03 12:33:47 2010 -0700 +++ b/text/blobdef.tex Thu Jun 03 17:19:37 2010 -0700 @@ -180,6 +180,8 @@ The $(-1)^{j+1}$ factors imply that the terms of $\bd^2(b)$ all cancel. Thus we have a chain complex. +Note that Property \ref{property:functoriality}, that the blob complex is functorial with respect to homeomorphisms, is immediately obvious from the definition. A homeomorphism acts in an obvious on blobs and on fields. + We define the {\it support} of a blob diagram $b$, $\supp(b) \sub X$, to be the union of the blobs of $b$. For $y \in \bc_*(X)$ with $y = \sum c_i b_i$ ($c_i$ a non-zero number, $b_i$ a blob diagram), diff -r eb03c4a92f98 -r 160ca7078ae9 text/intro.tex --- a/text/intro.tex Thu Jun 03 12:33:47 2010 -0700 +++ b/text/intro.tex Thu Jun 03 17:19:37 2010 -0700 @@ -328,9 +328,9 @@ \end{property} See \S \ref{sec:deligne} for an explanation of the terms appearing here. The proof will appear elsewhere. -Properties \ref{property:functoriality}, \ref{property:gluing-map} and \ref{property:skein-modules} will be immediate from the definition given in -\S \ref{sec:blob-definition}, and we'll recall them at the appropriate points there. \todo{Make sure this gets done.} -Properties \ref{property:disjoint-union} and \ref{property:contractibility} are established in \S \ref{sec:basic-properties}. +Properties \ref{property:functoriality} and \ref{property:skein-modules} will be immediate from the definition given in +\S \ref{sec:blob-definition}, and we'll recall them at the appropriate points there. +Properties \ref{property:disjoint-union}, \ref{property:gluing-map} and \ref{property:contractibility} are established in \S \ref{sec:basic-properties}. Property \ref{property:hochschild} is established in \S \ref{sec:hochschild}, Property \ref{property:evaluation} in \S \ref{sec:evaluation}, Property \ref{property:blobs-ainfty} as Example \ref{ex:blob-complexes-of-balls} in \S \ref{sec:ncats}, and Properties \ref{property:product} and \ref{property:gluing} in \S \ref{sec:ainfblob} as consequences of Theorem \ref{product_thm}.