Complex manifolds as families of homotopy algebras

Joan Millès (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Domaines: K-théorie et homologie [math.KT]; Topologie algébrique [math.AT]; Géométrie différentielle [math.DG]

Joan Millès. Complex manifolds as families of homotopy algebras. Rendiconti del Seminario Matematico della Università di Padova, 2018, 140, pp.129-172. ⟨10.4171/RSMUP/6⟩. ⟨hal-01105088⟩