From: Greg Kuperberg
Subject: For toplist
Date: Tue, 12 May 1998 16:40:27 -0700 (PDT)
> The idea is the following:
> C^*(X;Q) the singular cochain algebra is associative but
> not commutative
> over Q we can symmetrize it: u*v = 1/2 (u\cup v \pm v\cup u)
> etc
> claim is * is the beginning of an A_\infty algebra
> query: such that the m_i are sutiably symmetric?
>
> anyone know where the details are written down?
Obviously this is not an answer to Jim's question either, but I wanted
to mention a simple point which is related and possibly interesting.
If (and only if) a simplicial cochain on a simplicial complex is closed,
it can be extended to a constant differential form on each simplex.
Then the wedge product on such forms is a commutative, associative
algebra. It corresponds to a symmetrization of the cup product of the two
corresponding closed cochains. Namely it is the average of the different
simplicial cup products given by different orderings of the vertices.
On another note, here are some papers on homotopy algebras in the xxx
math archive.
math.QA/9805052. Masoud Khalkhali. Homology of
L_{\infty}-Algebras and Cyclic Homology. 8 pages. QA (KT).
math.QA/9805051. Masoud Khalkhali. On Cyclic
Homology of A_{\infty} Algebras. 16 pages. QA (KT).
math.QA/9802118. Dmitry Roytenberg, Alan
Weinstein. Courant Algebroids and Strongly Homotopy Lie Algebras. 10
pages. QA (DG).
hep-th/9711045. Martin Markl. Loop Homotopy
Algebras in Closed String Field Theory. 29 pages. (QA).
math.QA/9710144. Fusun Akman. A master identity
for homotopy Gerstenhaber algebras. 26 pages. (q-alg/9710004). QA.
math.QA/9702155. Vladimir Hinich. Homological
algebra of homotopy algebras. 39 pages. (q-alg/9702015). QA.
math.QA/9602149. Takashi Kimura (Boston
University), Alexander A. Voronov (University of Pennsylvania), Gregg
J. Zuckerman (Yale University). Homotopy Gerstenhaber algebras and
topological field theory. 29 pages. IHES/96 (q-alg/9602009). QA.
math.QA/9601158. Michael Penkava. Infinity
Algebras and the Homology of Graph Complexes. 14 pages.
(q-alg/9601018). QA.
math.QA/9512154. Michael Penkava. L-infinity
algebras and their cohomology. 28 pages. (q-alg/9512014). QA.
math.AG/9502006. Takashi Kimura, Jim Stasheff,
Alexander A. Voronov. Homology of moduli spaces of curves and
commutative homotopy algebras. 18 pages. (alg-geom/9502006). AG (QA).
hep-th/9409063. Murray Gerstenhaber, Alexander A.
Voronov. Homotopy G-algebras and moduli space operad. 12 pages.
Internat. Math. Research Notices (1995) 141-153. (DG).
As it happens, all but two are in category QA (Quantum Algebra) and none
are in AT (Algebraic Topology). I found these with the search query
title:(algebras and (homotopy or infty or infinity))
at the Front for the xxx Math Archive:
http://front.math.ucdavis.edu/