"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.