Complex manifolds as families of homotopy algebras

  • Joan Bellier-Millès

    Université Toulouse III Paul Sabatier, Toulouse, France

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.

Cite this article

Joan Bellier-Millès, Complex manifolds as families of homotopy algebras. Rend. Sem. Mat. Univ. Padova 140 (2018), pp. 129–172

DOI 10.4171/RSMUP/6