| Résume | An approach to construction of all genus Gromov-Witten invariants of compact Calabi-Yau manifolds in terms of A-infinity algebras/categories, developed in the works of the speaker, will be reviewed.
The construction is based on the following theorem: the Feynman transform of the twisted modular operad of associative algebras with scalar product coincides with the complex computing the cohomology of compactified moduli spaces of curves $\bar\mathcalM_g,n$ (“Modular operads and Batalin-Vilkovisky geometry” (MPIM Bonn 2006-48 (04/2006)). An important role in the construction is played also by the quantum master equation on the cyclic cochains, the solutions to which correspond to algebras over the specified Feynman transform. The cohomology classes constructed from the A-infinity algebras/categories define under certain conditions cohomological field theories. |
