arXiv subjects
Publications and source records attributed to Anna Sopena-Gilboy.
This paper explores a new context for operadic calculus and Koszul duality arising in the study of complex manifolds or, more abstractly, of bidifferential bigraded algebras up to pluripotential weak equivalence. In particular, we establish a Pluripotential Homotopy Transfer Theorem. This provides a homotopical framework for the theory of Massey products in Bott-Chern and Aeppli cohomologies, defined for any complex manifold.
We introduce a functor from cochain complexes to bicomplexes, called inflation functor, which sends quasi-isomorphisms to the class of pluripotential weak equivalences. We show this functor is part of a Quillen adjunction. Its right adjoint is a well-known construction in complex geometry, which gives a sheaf-theoretic presentation of Bott-Chern and Aeppli cohomologies. The inflation functor plays a key role in pluripotential Koszul duality theory for operads and allows us to construct the infinity-category of bicomplexes in the pluripotential sense.