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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] |
463 The singular chains of the $n$-dimensional surgery cylinder operad act on blob cochains. |
463 The singular chains of the $n$-dimensional surgery cylinder operad act on blob cochains |
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464 (up to coherent homotopy). |
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 |