Geometric structures and configurations of flags in orbits of real forms
Abstract
This is an introduction and a survey on geometric structures modelled on closed orbits of real forms acting on spaces of flags. We focus on
3-manifolds and the flag space of all pairs of a point and a line containing it
in $\mathbf P(\mathbf C^3)$. It includes a description of general flag structures which are not
necessarily flat and a combinatorial description of flat structures through con-
figurations of flags in closed orbits of real forms. We also review volume and
Chern-Simons invariants for those structures.
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