Hamilton, Alastair and Lazarev, Andrey (2008) Characteristic classes of $\ai$-algebras. Journal of Homotopy and Related Structures, 3 (1). pp. 65-111. ISSN 2193-8407Full text not available from this repository.
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 or Publication Title:||Journal of Homotopy and Related Structures|
|Subjects:||Q Science > QA Mathematics|
|Departments:||Faculty of Science and Technology > Mathematics and Statistics|
|Deposited On:||04 Nov 2012 14:46|
|Last Modified:||04 May 2016 00:00|
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