Quantum gravity, Geometry, Mathematical physics
This is an analysis of the geometrical aspects of the simplicial quantum gravity model known as the dynamical triangulations approach. An account is given to introduce the non-expert reader to the spirit of the subject and to provide a mathematical route to the heart of the matter for the expert. Linear manifolds and entropy estimates of the number of triangulations of three- and four-manifolds are discussed. Continuum physics is recovered through scaling limits and computer simulation is used to study simplicial quantum gravity.