Nijenhuis forms on L∞L∞-algebras and Poisson geometry

We investigate Nijenhuis deformations of L∞L∞-algebras, a notion that unifies several Nijenhuis deformations, namely those of Lie algebras, Lie algebroids, Poisson structures and Courant structures. Additional examples, linked to Lie n-algebras and n-plectic manifolds, are included.