Strong homotopy algebras for chiral higher spin gravity via Stokes theorem

A bstract Chiral higher spin gravity is defined in terms of a strong homotopy algebra of pre-Calabi-Yau type (noncommutative Poisson structure). All structure maps are given by the integrals over the configuration space of concave polygons and the first two maps are related to the (Shoikhet-Tsygan-)Kontsevich Formality. As with the known formality theorems, we prove the A ∞ -relations via Stokes’ theorem by constructing a closed form and a configuration space whose boundary components lead to the A ∞ -relations. This gives a new way to formulate higher spin gravities and hints at a construct encompassing the known formality theorems.