Vorträge in der Woche 30.10.2006 bis 05.11.2006

Montag, 30.10.2006: Arithmetic Manifolds

Nicolas Bergeron

Starting from Archimedes' Cattle Problem and Pell's equation I will introduce the notion of an arithmetic subgroup of a real orthogonal group. Such arithmetic groups may be used to construct compact hyperbolic manifolds in every dimension. In dimension 4, and up to surgery, these are essentially the only known constructions of negatively curved compact manifolds. In the second part of the talk I will introduce hyperplane sections of these arithmetic hyperbolic manifolds and explain how these can be used to study the topology of arithmetic hyperbolic manifolds in a way analogous to the classical Lefschetz' theorem for complex projective manifolds. I will focus on a recent joint work with Frederic Haglund and Dani Wise.