Manifolds with multiplication on the tangent sheaf

Yu. I. Manin

Manifolds with multiplication on the tangent sheaf

Algebraic Geometry 2007-05-23 v1 Differential Geometry

Authors: Yu. I. Manin

Abstract

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.

Keywords

frobenius algebra tangent bundle algebraic topology

Cite

@article{arxiv.math/0502578,
  title  = {Manifolds with multiplication on the tangent sheaf},
  author = {Yu. I. Manin},
  journal= {arXiv preprint arXiv:math/0502578},
  year   = {2007}
}

Comments

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

Manifolds with multiplication on the tangent sheaf

Abstract

Keywords

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