Seminar

Affine crystallographic and properly discontinuous groups

There is a long standing conjecture of Auslander (1964) which states that every a!ne crystallographic 

group has a solvable subgroup of finite index. Milnor (1977) asked if, more generally, every properly 

discontinuous a!ne group has a solvable subgroup of finite index. This more general conjecture was 

disproved by Margulis (1983). The Auslander conjecture has been proved in many cases, but is wide 

open for affine spaces of dimension at least 7.

This is the first one of two talks on our joint work with G.Margulis and G.Soifer. The second one will 

be given by G. Soifer. I will explain the notions and conjectures and will give an idea of the methods 

involved in the constructions and proofs in our joint work with Margulis and Soifer. The main tool are 

dynamics of linear and a!ne maps.