Ludovic Marquis
l'Ecole Normale Superieure de Lyon, France
February 11, 2010
Convex Projective Manifold of finite volume: In my talk, I will explain how convex projective geometry is a generalisation of hyperbolic geometry.
l'Ecole Normale Superieure de Lyon, France
February 11, 2010
Convex Projective Manifold of finite volume: In my talk, I will explain how convex projective geometry is a generalisation of hyperbolic geometry.
A convex projective manifold $M$ is the quotient of a properly open convex Omega set by a discrete group of projective transformation $G$. The basic example of such manifold is the quotient of the hyperbolic space by a discrete group of isometries.
This kind of manifold carry a natural measure. A lot of people have studied the case where the manifold $M$ is compact. I will explain what is known when the dimension of $M$ is 2 and how to construct such a manifold when Omega is not the hyperbolic space.
This will lead us, to the construction of discrete subgroup of $SL(n+1,R)$ which are Zariski dense but not lattice of $SL(n+1,R)$.