Manifolds with multiplication on the tangent sheaf

Abstract

This talk reviews the current state of the theory of F–(super)manifolds (M, ◦), first defined in [6] and further developed in [5], [11], [12]. Here ◦ is an OM–bilinear multiplication on the tangent sheaf T_M, satisfying an integrability condition. F–manifolds and compatible flat structures on them furnish a useful weakening of Dubrovin’s Frobenius structure which naturally arises in the quantum K–theory, theory of extended moduli spaces, and unfolding spaces of singularities.

Keywords

• f-manifolds
• frobenius manifolds
• flat connections
• dubrovin’s duality