ν-Tamari lattices via subword complexes

We show that the ν-Tamari lattices of Préville-Ratelle and Viennot can obtained as the duals of certain subword complexes. This generalizes a known result for the classical Tamari lattice, provides a simple description of the lattice property using certain bracket vectors of ν-trees, and gives (conjectural) insight on the geometry of more general objects in terms of polytopal subdivisions of multiassociahedra.