SÉMINAIRE DE GÉOMÉTRIE

Vendredi, 16 juin 2000 10:30 – 11:30 Salle 2 , Laboratoire MPB

John RATCLIFFE , Vanderbilt University

“ On the growth of the number of hyperbolic

gravitational instantons with respect to volume ”

Résumé :

A hyperbolic gravitational instanton is a closed orientable hyperbolic 4-manifold that is obtained by doubling a compact orientable hyperbolic 4-manifold with a totally geodesic boundary. We show that the number of hyperbolic gravitational instantons grows superexponentially with respect to volume. As an application, we show that the Hartle-Hawking wave function for the universe is infinitely peaked at a certain closed hyperbolic 3-manifold. This is joint work with Steven Tschantz.