458 The proof appears in \S \ref{sec:map-recon}.

   458 The proof appears in \S \ref{sec:map-recon}.

   459 

   459 

   460 \newtheorem*{thm:deligne}{Theorem \ref{thm:deligne}}

   460 \newtheorem*{thm:deligne}{Theorem \ref{thm:deligne}}

   461 

   461 

   462 \begin{thm:deligne}[Higher dimensional Deligne conjecture]

   462 \begin{thm:deligne}[Higher dimensional Deligne conjecture]

   464 Since the little $n{+}1$-balls operad is a suboperad of the $n$-dimensional surgery cylinder operad,

   465 Since the little $n{+}1$-balls operad is a suboperad of the $n$-dimensional surgery cylinder operad,

   465 this implies that the little $n{+}1$-balls operad acts on blob cochains of the $n$-ball.

   466 this implies that the little $n{+}1$-balls operad acts on blob cochains of the $n$-ball.

   466 \end{thm:deligne}

   467 \end{thm:deligne}

   467 See \S \ref{sec:deligne} for a full explanation of the statement, and the proof.

   468 See \S \ref{sec:deligne} for a full explanation of the statement, and the proof.

   468 

   469