diff -r 11532ce39ec0 -r 4f008d0a29d4 text/intro.tex --- a/text/intro.tex Wed Sep 22 20:42:47 2010 -0700 +++ b/text/intro.tex Thu Sep 23 10:03:26 2010 -0700 @@ -431,7 +431,7 @@ \subsection{Applications} \label{sec:applications} -Finally, we give two theorems which we consider applications. % or "think of as" +Finally, we give two applications of the above machinery. \newtheorem*{thm:map-recon}{Theorem \ref{thm:map-recon}} @@ -444,18 +444,21 @@ \end{thm:map-recon} This says that we can recover (up to homotopy) the space of maps to $T$ via blob homology from local data. +Note that there is no restriction on the connectivity of $T$. The proof appears in \S \ref{sec:map-recon}. \newtheorem*{thm:deligne}{Theorem \ref{thm:deligne}} \begin{thm:deligne}[Higher dimensional Deligne conjecture] -The singular chains of the $n$-dimensional fat graph operad act on blob cochains. +The singular chains of the $n$-dimensional surgery cylinder operad act on blob cochains. +Since the little $n{+}1$-balls operad is a suboperad of the $n$-dimensional surgery cylinder operad, +this implies that the little $n{+}1$-balls operad acts on blob cochains of the $n$-ball. \end{thm:deligne} See \S \ref{sec:deligne} for a full explanation of the statement, and the proof. -\noop{ +\noop{ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Future directions} \label{sec:future} \nn{KW: Perhaps we should delete this subsection and salvage only the first few sentences.} @@ -482,7 +485,7 @@ but haven't investigated the details. Most importantly, however, \nn{applications!} \nn{cyclic homology, $n=2$ cases, contact, Kh} \nn{stabilization} \nn{stable categories, generalized cohomology theories} -} %%% end \noop +} %%% end \noop %%%%%%%%%%%%%%%%%%%%% \subsection{Thanks and acknowledgements} % attempting to make this chronological rather than alphabetical