diff -r cfab8c2189a7 -r 576466ef9a68 text/smallblobs.tex
--- a/text/smallblobs.tex	Sun Nov 01 21:40:23 2009 +0000
+++ b/text/smallblobs.tex	Tue Nov 03 02:18:10 2009 +0000
@@ -28,7 +28,7 @@
 
 In fact, for a fixed $\beta$, $\Diff{M}$ retracts onto the subset $\setc{\varphi \in \Diff{M}}{\text{$\varphi(\beta)$ is subordinate to $\cU$}}$.
 \end{claim}
-\todo{Ooooh, I hope that's true.}
+\nn{need to check that this is true.}
 
 We'll need a stronger version of Property \ref{property:evaluation}; while the evaluation map $ev: \CD{M} \tensor \bc_*(M) \to \bc_*(M)$ is not unique, it has an up-to-homotopy representative (satisfying the usual conditions) which restricts to become a chain map $ev: \CD{M} \tensor \bc^{\cU}_*(M) \to \bc^{\cU}_*(M)$. The proof is straightforward: when deforming the family of diffeomorphisms to shrink its supports to a union of open sets, do so such that those open sets are subordinate to the cover.