Operads, deformation theory and F-manifolds

By Sergei A. Merkulov. 2002

51 citations recorded by the source corpus.

Probenius manifolds created by Dubrovin in 1991 from rich theoretical physics material have been found since in many different fragments of mathematics — quantum cohomology and mirror symmetry, complex geometry, symplectic geometry, singularity theory, integrable systems — raising hopes for unifying them into one picture. It also became clear that the notion of Probenius manifold is not broad enough to cover all objects of the associated working categories; say, on the B-side of the mirror symmetry it applies only to extended moduli spaces of Calabi-Yau manifolds, the latter forming a rather small subcategory of the category of complex manifolds.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a5bc45c44c9a2cd671923813d332c7500a366e1c