Complex manifolds as families of homotopy algebras

Joan Millès

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arXiv · 1409.3604

Complex manifolds as families of homotopy algebras

Joan Millès

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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.

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Joan Millès. 2014-09-11. Complex manifolds as families of homotopy algebras. https://arxiv.org/abs/1409.3604

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