The Homology of Pseudo-Riemannian Geometries and Implications for Quantum Gravity

Dr. Robert D. Preece

Department of Physics
UAHuntsville

28 January 2011
218 Shelby Center
3:00 (Refreshements at 2:30)

Abstract

The homology classes of a manifold are topological invariants that give clues to globalstruct ure. Meanwhile, in physics, the playground for gravity is the pseudo-RiemannianGeometry (PRG) of four-dimensional spacetime solutions to General Relativity. These are manifolds that do not have a positive-definite metric, as the sign for the timecomponent in the distance differs from that of the spatial components. In particular, light rays follow null vectors (of zero length), so for each point of spacetime, we can define three equivalence classes: based upon null, spacelike and timelike separations. Because the metric is not positive-definite, the entire homology classification for PRG has only recently been derived. I will discuss this classification and indicate how there may be a relationship between the 2D homology class of PRG and the representations of the solutions found in various proposals for quantizing gravity.