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Characteristic classes of $\ai$-algebras
#
Characteristic classes of $\ai$-algebras

##
Alastair Hamilton and Andrey Lazarev

A standard combinatorial construction, due to Kontsevich, associates to any
$\ai$-algebra with an invariant inner product, an inhomogeneous class in the
cohomology of the moduli spaces of Riemann surfaces with marked points.
We propose an alternative version of this construction based on noncommutative
geometry and use it to prove that homotopy equivalent algebras give rise to
the same cohomology classes. Along the way we re-prove Kontsevich's theorem
relating graph homology to the homology of certain infinite-dimensional Lie
algebras. An application to topological conformal field theories is given.

Journal of Homotopy and Related Structures, Vol. 3(2008), No. 1, pp. 65-111