Non-algebraic Anosov flows in higher dimensions

Anosov flows are prototypical examples of hyperbolic dynamics that preserve invariant uniformly contracting and expanding distributions. We recall the classification of algebraic Anosov flows by Per Tomter and currently known examples of non-algebraic Anosov flows. We give a construction of non-algebraic Anosov flows in higher dimensions that fibres over the recent Fenley—Mann—Potrie example of dimension 4, which relies on arithmetic Kleinian groups acting on torus.