"Geometry and Analysis on Groups" Research Seminar

Time: 2015.10.20, 15:00--17:00
Location: Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock
Title: "Anosov maps on nilmanifolds."
Speaker: Tracy Payne (Idaho State University)
Abstract: A diffeomorphism of a compact manifold is called Anosov if at each point in the manifold, the tangent space is the sum of contracting and expanding directions for the mapping. Anosov diffeomorphisms are archetypal examples of "chaotic" maps. Up to conjugacy and finite covers, all known examples of Anosov maps are defined by hyperbolic automorphisms of nilpotent Lie groups which preserve a lattice in the group. At the Lie algebra level, an Anosov automorphism of a nilpotent Lie algebra is an automorphism preserving a rational structure and having no eigenvalues of modulus one. We will explain how to construct examples of Anosov diffeomorphisms of nilmanifolds and their finite quotients, and we will present properties of Anosov automorphisms and a description of the structure of associated Lie algebras. We will also discuss generalizations to the classes of partially hyperbolic automorphisms and finite-order automorphisms of rational nilpotent Lie algebras.