Fixed points of multimaps on infra-nilmanifolds

Infra-nilmanifolds are determined up to diffeomorphism by their fundamental group, which is a finitely generated torsionfree nilpotent-by-finite group and moreover all such groups do appear as the fundamental group of such an infra-nilmanifold. It follows that many geometric properties of these manifolds can be determined from the algebraic structure of their fundamental group. Via this PhD project it is our intention to focus on this algebraic approach in the study of multimaps. These are maps for which any element has several images, just like for example taking the square root in the complex plane is a 2-valued map (if one excludes the orgin). We will develop methods to compute Nielsen type numbers for such multimaps, from which we can then deduce information on fixed points, periodic points,...