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Characteristic classes of $\ai$-algebras

Hamilton, Alastair and Lazarev, Andrey (2008) Characteristic classes of $\ai$-algebras. Journal of Homotopy and Related Structures, 3 (1). pp. 65-111. ISSN 2193-8407

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Abstract

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.

Item Type: Article
Journal or Publication Title: Journal of Homotopy and Related Structures
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 59741
Deposited By: ep_importer_pure
Deposited On: 04 Nov 2012 14:46
Refereed?: Yes
Published?: Published
Last Modified: 01 Apr 2014 11:54
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/59741

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