--- a/text/deligne.tex Fri May 28 15:20:11 2010 -0700
+++ b/text/deligne.tex Fri May 28 16:28:47 2010 -0700
@@ -11,7 +11,13 @@
(Proposition \ref{prop:deligne} below).
Then we sketch the proof.
-The usual Deligne conjecture \nn{need refs} gives a map
+\nn{Does this generalisation encompass Kontsevich's proposed generalisation from \cite{MR1718044}, that (I think...) the Hochschild homology of an $E_n$ algebra is an $E_{n+1}$ algebra? -S}
+
+%from http://www.ams.org/mathscinet-getitem?mr=1805894
+%Different versions of the geometric counterpart of Deligne's conjecture have been proven by Tamarkin [``Formality of chain operad of small squares'', preprint, http://arXiv.org/abs/math.QA/9809164], the reviewer [in Confˇrence Moshˇ Flato 1999, Vol. II (Dijon), 307--331, Kluwer Acad. Publ., Dordrecht, 2000; MR1805923 (2002d:55009)], and J. E. McClure and J. H. Smith [``A solution of Deligne's conjecture'', preprint, http://arXiv.org/abs/math.QA/9910126] (see also a later simplified version [J. E. McClure and J. H. Smith, ``Multivariable cochain operations and little $n$-cubes'', preprint, http://arXiv.org/abs/math.QA/0106024]). The paper under review gives another proof of Deligne's conjecture, which, as the authors indicate, may be generalized to a proof of a higher-dimensional generalization of Deligne's conjecture, suggested in [M. Kontsevich, Lett. Math. Phys. 48 (1999), no. 1, 35--72; MR1718044 (2000j:53119)].
+
+
+The usual Deligne conjecture (proved variously in \cite{MR1805894, MR2064592, hep-th/9403055, MR1805923} gives a map
\[
C_*(LD_k)\otimes \overbrace{Hoch^*(C, C)\otimes\cdots\otimes Hoch^*(C, C)}^{\text{$k$ copies}}
\to Hoch^*(C, C) .