Smooth conjugacy for codimension 1 Anosov diffeomorphisms

In this talk we shall present joint work with A. Gogolev on some rigidity results in the setting of codimension one Anosov diffeomorphisms on manifols of dimension larger than or equal to 3. This result is a further development of our program with Andrey of classiying smooth conjugacy via matching of jacobians. Even though the data is much coarser than the usual matching of derivatives it results in a more stable theory.