Complex manifolds as families of homotopy algebras
Joan Bellier-Millès
Université Toulouse III Paul Sabatier, Toulouse, France
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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