A(infinity) algebras and the cohomology of moduli spaces
Aug 12, 1994Citations per year
Abstract:
We introduce the notion of cyclic cohomology of an algebra and show that the deformations of an A_\infinity algebra which preserve an invariant inner product are classified by means of cyclic cohomology. We use this result to construct some cycles on the moduli space of algebraic curves. The paper also contains a review of some well known notions and results about Hochschild and cyclic cohomology of associative algebras, A_\infinity algebras, deformation theory of algbras. We also include some appendices dealing with the homology of the graph complex associated to the moduli space, and a a more detailed proof of the results in the main part. These appendices, which are not intended for publication, can be omitted in printing the paper. The appendices include some figures, which are included in the compressed file submitted.References(8)
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