Description:
<jats:title>Abstract</jats:title><jats:p>Geometric structures on a manifold <jats:italic>M</jats:italic> arise from a covering of <jats:italic>M</jats:italic> by charts with values in a homogeneous space <jats:italic>G</jats:italic>/<jats:italic>H</jats:italic>, with chart transitions restrictions of elements of <jats:italic>G</jats:italic>. If <jats:italic>M</jats:italic> is aspherical, then such geometric structures are given by a homomorphism of the fundamental group of <jats:italic>M</jats:italic> into <jats:italic>G</jats:italic>. Rigidity of such structures means that the conjugacy class of the homomorphism can be reconstructed from topological or geometric information on <jats:italic>M</jats:italic>. We give an overview of such rigidity results, focusing on topological type and length functions.</jats:p>