Vanishing of cohomology and parameter rigidity of actions of solvable Lie groups, II

The paper proves that the right AN-action on Γ\G is parameter rigid under the stated higher-rank hypotheses (Theorem 2) by combining a cohomological rigidity criterion, computations of H1 with appropriate coefficients, and a large-scale geometric step using quasi-isometry rigidity of symmetric spaces; see the statement and proof outline in the introduction and Sections 2–4 . The candidate solution follows the same architecture: it introduces the cocycle aρ(x,·) (paper’s aρ), rigidifies the A-part via quasi-isometry rigidity (Kleiner–Leeb/Pansu) and then constrains the N-part by a-equivariance and Lie brackets, finally solving a leafwise cohomological equation to produce the transfer map and automorphism; this mirrors the paper’s Proposition 6 and the reduction to Proposition 13 and their treatment via quasi-isometries and cohomology with λ-coefficients . Minor gaps in the candidate’s write-up (e.g., implicit use of simply connected leaves when constructing the transfer map) are handled in the paper by the leafwise cohomology framework, but the essential steps and hypotheses align.