Characteristic classes of A-infinity algebras
Alastair Hamilton, Andrey Lazarev

TL;DR
This paper introduces a noncommutative geometric approach to characteristic classes of A-infinity algebras, proving invariance under homotopy and relating graph homology to Lie algebra homology, with applications to topological field theories.
Contribution
It provides an alternative construction of characteristic classes using noncommutative geometry and proves their invariance under homotopy, extending Kontsevich's theorem.
Findings
Homotopy equivalent A-infinity algebras produce the same cohomology classes.
Re-proved Kontsevich's theorem linking graph homology to Lie algebra homology.
Applied the theory to topological conformal field theories.
Abstract
A standard combinatorial construction, due to Kontsevich, associates to any A-infinity algebra with an invariant inner product, an inhomogeneous class in the cohomology of the moduli spaces of Riemann surfaces with marked points. We describe 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models
