Barannikov, Sergey; Kontsevich, Maxim Frobenius manifolds and formality of Lie algebras of polyvector fields. (English) Zbl 0914.58004 Int. Math. Res. Not. 1998, No. 4, 201-215 (1998). Starting with a differential graded Lie algebra \(t\) and its associated formal (graded) moduli space \({\mathcal M}_t\), the authors define the structure of a formal Frobenius manifold on the graded vector space \(H^*(M,\Lambda^* T_M)\), where \(M\) denotes the underlying connected compact complex manifold. There is a conjecture about relations of the constructed Frobenius manifold to Gromov-Witten invariance of the dual manifold \(\widetilde M\).The paper is organized as follows: Introduction; 1. Frobenius manifolds; 2. Moduli spaces via deformation functors; 3. Algebraic structure of the tangent sheaf of the moduli space; 4. Integral; 5. Metric on \({\mathcal T}_M\); 6. Flat coordinates on moduli space; 7. Flat connection and periods; 8. Scaling transformations; 9. Further developments; Appendix. Reviewer: H.Boseck (Greifswald) Cited in 11 ReviewsCited in 79 Documents MSC: 58D27 Moduli problems for differential geometric structures 32G13 Complex-analytic moduli problems 17B66 Lie algebras of vector fields and related (super) algebras Keywords:deformations; moduli spaces; Frobenius manifold × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL