Complex manifolds as families of homotopy algebras

Abstract

We prove an equivalence of categories from formal complex structures with formal holomorphic maps to homotopy algebras over a simple operad with its associated homotopy morphisms. We extend this equivalence to complex manifolds. A complex structure on a smooth manifold corresponds in this way to a family of algebras indexed by the points of the manifold.

Introduction and text improved, Frölicher-Nijenhuis bracket corrected. 31 pages

Cited by in corpus (1)

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