ON CODIMENSION ONE PARTIALLY HYPERBOLIC DIFFEOMORPHISMS

The paper’s Theorem A establishes that for any codimension-one partially hyperbolic diffeomorphism f: N → N, (i) N ≅ T^n, (ii) the 1D center Ec is locally uniquely integrable, and (iii) f is semiconjugate to a linear codimension-one Anosov automorphism f∗ induced on π1(N), with proofs via hyperplanar foliations, quasi-isometry/global product structure, and a Franks semiconjugacy (see Theorem A and its road map; Sections 2–4 and 5) . The candidate solution follows the same overall structure: HPS foliation theory for Eu, center integrability under codimension-one domination, torus topology via the lifted hyperplanar foliation and global product structure, and Franks’ semiconjugacy—matching the paper’s steps. Minor issues: the model compresses (and partially cites the very paper) for key steps (torus classification and linear hyperbolicity), making parts circular, and omits some technicalities (e.g., foliation holonomy/leaf-space arguments), but the core argument is aligned with the paper’s and correct at the stated level.