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minor - Section 3.2
authorKevin Walker <kevin@canyon23.net>
Thu, 08 Dec 2011 15:57:34 -0800
changeset 939 e3c5c55d901d
parent 938 082bfb8f6325
child 940 04079a7aeaef
minor - Section 3.2
blob to-do file | annotate | diff | comparison | revisions
blob_changes_v3 file | annotate | diff | comparison | revisions
text/basic_properties.tex file | annotate | diff | comparison | revisions 
--- a/blob to-do	Thu Dec 08 12:06:43 2011 -0800
+++ b/blob to-do	Thu Dec 08 15:57:34 2011 -0800
@@ -4,6 +4,9 @@
 * add "homeomorphism" spiel befure the first use of "homeomorphism in the intro
 * maybe also additional homeo warnings in other sections
 
+* Lemma 3.2.3 (\ref{support-shrink}) implicitly assumes embedded (non-self-intersecting) blobs. this can be fixed, of course, but it makes the arument more difficult to understand
+
+
 
 ====== minor/optional ======
 
--- a/blob_changes_v3	Thu Dec 08 12:06:43 2011 -0800
+++ b/blob_changes_v3	Thu Dec 08 15:57:34 2011 -0800
@@ -37,4 +37,5 @@
 - small corrections to proof of product theorem (7.1.1)
 - added remarks that various homotopy equivalences we construct are well-defined up to a contractible set of choices
 - clarified that the surgery cylinder operad action is only up to coherent homotopy
+- added some details to the construction of a traditional 2-category from a disk-like 2-category
 
--- 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.
blob