Frobenius_infinity invariants of homotopy Gerstenhaber algebras I
Abstract
We construct a functor from the derived category of homotopy Gerstenhaber algebras with finitedimensional cohomology to the purely geometric category of socalled $F_{\infty}$manifolds. The latter contains Frobenius manifolds as a subcategory (so that a pointed Frobenius manifold is itself a homotopy Gerstenhaber algebra). If a homotopy Gerstenhaber algebra happens to be formal as a $L_{\infty}$algebra, then its $F_{\infty}$manifold comes equipped with the GaussManin connection. Mirror Symmetry implications are discussed.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2000
 arXiv:
 arXiv:math/0001007
 Bibcode:
 2000math......1007M
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Differential Geometry
 EPrint:
 More details on the relationship between formality maps and GauusManin connections are given in Sect.2.7