# HG changeset patch
# User Scott Morrison <scott@tqft.net>
# Date 1275627595 25200
# Node ID f77cb464248e4e41d3f463ba9893e0c7260d1a09
# Parent  7a5a73ec89617cb568c50cf3e7d4fa0d57b380c1
finally understanding what Lurie says, fixed remark about maps to a space

diff -r 7a5a73ec8961 -r f77cb464248e blob1.tex
--- a/blob1.tex	Thu Jun 03 21:16:36 2010 -0700
+++ b/blob1.tex	Thu Jun 03 21:59:55 2010 -0700
@@ -43,6 +43,7 @@
 \item[A] may need to weaken statement to get boundaries working (K) finish
 \item[B] (S) look at this, decide what to keep
 
+\item Work in the references Chris Douglas gave us on the classification of local field theories, \cite{BDH-seminar,DSP-seminar,schommer-pries-thesis,0905.0465}.
 \item Make clear exactly what counts as a "blob diagram", and search for
 "blob diagram"
 
diff -r 7a5a73ec8961 -r f77cb464248e text/a_inf_blob.tex
--- a/text/a_inf_blob.tex	Thu Jun 03 21:16:36 2010 -0700
+++ b/text/a_inf_blob.tex	Thu Jun 03 21:59:55 2010 -0700
@@ -357,9 +357,7 @@
 $$\cB^\cT(M) \simeq C_*(\Maps(M\to T)).$$
 \end{thm}
 \begin{rem}
-\nn{This just isn't true, Lurie doesn't do this! I just heard this from Ricardo...}
-\nn{KW: Are you sure about that?}
-Lurie has shown in \cite{0911.0018} that the topological chiral homology of an $n$-manifold $M$ with coefficients in \nn{a certain $E_n$ algebra constructed from $T$} recovers  the same space of singular chains on maps from $M$ to $T$, with the additional hypothesis that $T$ is $n-1$-connected. This extra hypothesis is not surprising, in view of the idea that an $E_n$ algebra is roughly equivalent data as an $A_\infty$ $n$-category which is trivial at all but the topmost level.
+Lurie has shown in \cite[Theorem 3.8.6]{0911.0018} that the topological chiral homology of an $n$-manifold $M$ with coefficients in a certain $E_n$ algebra constructed from $T$ recovers  the same space of singular chains on maps from $M$ to $T$, with the additional hypothesis that $T$ is $n-1$-connected. This extra hypothesis is not surprising, in view of the idea described in Example \ref{ex:e-n-alg} that an $E_n$ algebra is roughly equivalent data to an $A_\infty$ $n$-category which is trivial at all but the topmost level. Ricardo Andrade also told us about a similar result.
 \end{rem}
 
 \nn{proof is again similar to that of Theorem \ref{product_thm}.  should probably say that explicitly}