--- a/text/basic_properties.tex Mon Jun 28 08:54:36 2010 -0700
+++ b/text/basic_properties.tex Mon Jun 28 10:03:13 2010 -0700
@@ -95,19 +95,19 @@
For the next proposition we will temporarily restore $n$-manifold boundary
conditions to the notation.
-Let $X$ be an $n$-manifold, $\bd X = Y \cup (-Y) \cup Z$.
+Let $X$ be an $n$-manifold, $\bd X = Y \cup Y \cup Z$.
Gluing the two copies of $Y$ together yields an $n$-manifold $X\sgl$
with boundary $Z\sgl$.
-Given compatible fields (boundary conditions) $a$, $b$ and $c$ on $Y$, $-Y$ and $Z$,
+Given compatible fields (boundary conditions) $a$, $b$ and $c$ on $Y$, $Y$ and $Z$,
we have the blob complex $\bc_*(X; a, b, c)$.
-If $b = -a$ (the orientation reversal of $a$), then we can glue up blob diagrams on
+If $b = a$, then we can glue up blob diagrams on
$X$ to get blob diagrams on $X\sgl$.
This proves Property \ref{property:gluing-map}, which we restate here in more detail.
\textbf{Property \ref{property:gluing-map}.}\emph{
There is a natural chain map
\eq{
- \gl: \bigoplus_a \bc_*(X; a, -a, c) \to \bc_*(X\sgl; c\sgl).
+ \gl: \bigoplus_a \bc_*(X; a, a, c) \to \bc_*(X\sgl; c\sgl).
}
The sum is over all fields $a$ on $Y$ compatible at their
($n{-}2$-dimensional) boundaries with $c$.