Finite volume projective manifolds

Abstract

A convex real projective manifold or orbifold is \(M/G\), where \(M\) is the interior of a compact convex set in real projective space disjoint from some hyperplane and \(G\) is a discrete group of projective transformations which preserves \(M\). The manifold is strictly convex if there is no line segment in the boundary of \(M\). Strictly convex structures have many similarities to hyperbolic structures, particularly in the finite volume case. By contrast, properly convex structures are far more general.

I will discuss aspects of projective manifolds from the perspective of a low-dimensional topologist, giving a snap-shot of the material in the paper arXiv:1109.0585 with Cooper and Long.