Building blocks for topology change in 3D

Abstract

We investigate topology change in 3D. Using Morse theory and handle decomposition we find the set of elementary cobordisms for 3-manifolds. These are: (i) Ø<-> S^2; (ii) Σ_g <-> Σ_{g+1}; (iii) Σ_{g_1} \sqcup Σ_{g_2} <-> Σ_{g_1+g_2} and they have appealing physical interpretations, e.g. Big Bang/Big Crunch, wormhole creation/annihilation and Einstein-Rosen bridge creation/annihilation, respectively. This decomposition into building blocks can be used in the path integral approach to quantum gravity in the sum over topologies.

12 pages, LaTeX, 13 figures, uses epsf