Cocycles in Lie Groups, Cochains and Regularity Problem

The uploaded paper (a survey) states the Pollicott–Walkden non-abelian Livšic theorem with the definitions of µs, µu, θ̃ and θ̃′ and the periodic obstruction, and asserts existence of a Hölder transfer Φ under θ ∈ (θ̃′,1) and the cross inequalities, citing the original source; it does not supply a full proof but its statements match the literature and are internally consistent as a summary . The model’s solution gives a standard holonomy-based proof sketch that matches those hypotheses and reaches the same conclusion. There is a minor sign-direction slip in Step 2 of the model outline (claiming µs < λs^{θ−ε}), which is stronger than needed and not generally implied; however, the core summability/holonomy construction uses the correct cross-bunching and periodic-obstruction arguments, so the proof sketch remains valid after this correction. Overall: same theorem, consistent assumptions, different (sketched) proof; both are correct.