Frobenius_infinity invariants of homotopy Gerstenhaber algebras I

Details Frobenius_infinity invariants of homotopy Gerstenhaber algebras I Frobenius_infinity invariants of homotopy Gerstenhaber algebras I

2000-01-03

arxiv.org/abs/math/0001007v3

Duke Math. J. 105 (2000) , 411-461.

Mathematics

Algebraic Geometry

More details on the relationship between formality maps and Gauus-Manin connections are given in Sect.2.7

Scientific paper

We construct a functor from the derived category of homotopy Gerstenhaber algebras with finite-dimensional cohomology to the purely geometric category of so-called $F_{\infty}$-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 Gauss-Manin connection. Mirror Symmetry implications are discussed.

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