Infra-nilmanifolds and their fundamental groups (Q2762644)

The authors present a survey of results obtained for infra-nilmanifolds, their fundamental groups and some of their generalizations. One of the main focal points of their survey is the work on polynomial structures. A polynomial structure on a group \(\Gamma\) is a homomorphism \(\rho\) of \(\Gamma\) into the group of polynomial homomorphisms of \(\mathbb{R}^n\) such that the induced action of \(\Gamma\) on \(\mathbb{R}^n\) is properly discontinuous and has compact quotient \(\rho(\Gamma)\backslash\mathbb{R}^n\). A second focal point of the survey are Anosov diffeomorphisms and expanding maps on infra-nilmanifolds.