Pluripotential Homotopy Theory

Abstract

We build free, bigraded bidifferential algebra models for the forms on a complex manifold, with respect to a strong notion of quasi-isomorphism and compatible with the conjugation symmetry. This answers a question of Sullivan. The resulting theory naturally accomodates higher operations involving double primitives. As applications, we obtain various refinements of the homotopy groups, sensitive to the complex structure. Under a simple connectedness assumption, one obtains minimal models which are unique up to isomorphism and allow for explicit computations of the new invariants.

Updates following referee comments. To appear in Adv. Math. Comments welcome!

References in corpus (7)

• Geometry of nilmanifolds with left-invariant complex structure and deformations in the large
• On Bott-Chern cohomology and formality
• On the Structure of Double Complexes
• A faithful braid group action on the stable category of tricomplexes
• Model category structures and spectral sequences
• Dolbeault and Bott-Chern formalities: deformations and $\partial \overline{\partial }$-lemma
• Bigraded notions of formality and Aeppli-Bott-Chern-Massey products

Cited by in corpus (1)

• Some computations on trivial canonical-bundle solvmanifolds