Manifolds with multiplication on the tangent sheaf
Abstract
Description
This is a survey of the current state of the theory of $F$--(super)manifolds $(M,\circ)$, first defined in [HeMa] and further developed in [He], [Ma2], [Me1]. Here $\circ$ is an $\Cal{O}_M$--bilinear multiplication on the tangent sheaf $\Cal{T}_M$, 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.
16 pages. Talk at the Conference dedicated to the memory of B. Segre, Inst. Mat. Guido Castelnuovo, Rome, June 2004
16 pages. Talk at the Conference dedicated to the memory of B. Segre, Inst. Mat. Guido Castelnuovo, Rome, June 2004