Building blocks for topology change in 3D
Abstract
Description
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
12 pages, LaTeX, 13 figures, uses epsf