Manifolds with multiplication on the tangent sheaf

2005/02/28 by Yu. I. Manin, Manin, Yu. I.
Mathematics · #14H10 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #math.AG #math.DG #msc:14H10

paper · pdf · doi:10.48550/arxiv.math/0502578

16 pages. Talk at the Conference dedicated to the memory of B. Segre, Inst. Mat. Guido Castelnuovo, Rome, June 2004

arxiv created 2005/02/28 · arxiv updated 2009/12/01

Abstract

This is a survey of the current state of the theory of F--(super)manifolds (M,∘), first defined in [HeMa] and further developed in [He], [Ma2], [Me1]. Here ∘ is an \CalO_M--bilinear multiplication on the tangent sheaf \CalT_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.

Related

• Multiplication on the tangent bundle
• F‐Manifolds and geometry of information
• F-manifolds with flat structure and Dubrovin's duality
• Weak Frobenius manifolds
• On axioms of Frobenius like structure in the theory of arrangements