# Finite volume projective manifolds

Stephan Tillmann
University of Sydney
20 June 2012, 12 noon - 1pm, Carslaw 175, University of Sydney

## 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.