adding some biblio entries re: Deligne. Run svn up bibliography to update the bibliography, which is still in SVN
authorScott Morrison <scott@tqft.net>
Fri, 28 May 2010 16:28:47 -0700
changeset 292 7d0c63a9ce05
parent 291 9b8b474e272c
child 293 fc1e49660173
adding some biblio entries re: Deligne. Run svn up bibliography to update the bibliography, which is still in SVN
text/deligne.tex
text/intro.tex
--- 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) .
--- a/text/intro.tex	Fri May 28 15:20:11 2010 -0700
+++ b/text/intro.tex	Fri May 28 16:28:47 2010 -0700
@@ -287,7 +287,7 @@
 In most of the places where we say ``set" or ``vector space", any symmetric monoidal category would do. We could presumably also replace many of our chain complexes with topological spaces (or indeed, work at the generality of model categories), and likely it will prove useful to think about the connections between what we do here and $(\infty,k)$-categories.
 More could be said about finite characteristic (there appears in be $2$-torsion in $\bc_1(S^2, \cC)$ for any spherical $2$-category $\cC$, for example). Much more could be said about other types of manifolds, in particular oriented, $\operatorname{Spin}$ and $\operatorname{Pin}^{\pm}$ manifolds, where boundary issues become more complicated. (We'd recommend thinking about boundaries as germs, rather than just codimension $1$ manifolds.) We've also take the path of least resistance by considering $\operatorname{PL}$ manifolds; there may be some differences for topological manifolds and smooth manifolds.
 
-Many results in Hochschild homology can be understood `topologically' via the blob complex. For example, we expect that the shuffle product on the Hochschild homology of a commutative algebra $A$ simply corresponds to the gluing operation on $\bc_*(S^1 \times [0,1], A)$, but haven't investigated the details.
+Many results in Hochschild homology can be understood `topologically' via the blob complex. For example, we expect that the shuffle product on the Hochschild homology of a commutative algebra $A$ (see \cite[\S 4.2]{MR1600246}) simply corresponds to the gluing operation on $\bc_*(S^1 \times [0,1], A)$, but haven't investigated the details.
 
 Most importantly, however, \nn{applications!} \nn{cyclic homology, $n=2$ cases, contact, Kh}