Topology change in ISO(2,1) Chern-Simons gravity

Abstract

In 2+1 dimensional gravity, a dreibein and the compatible spin connection can represent a space-time containing a closed spacelike surface $\Sigma$ only if the associated SO(2,1) bundle restricted to $\Sigma$ has the same non-triviality (Euler class) as that of the tangent bundle of $\Sigma .$ We impose this bundle condition on each external state of Witten's topology-changing amplitude. The amplitude is non-vanishing only if the combination of the space topologies satisfies a certain selection rule. We construct a family of transition paths which reproduce all the allowed combinations of genus $g\ge 2$ spaces.

24 pages and 4 figures (not included)

Cited by in corpus (6)

• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
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• Topology Change in (2+1)-Dimensional Gravity
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• Interpolating Between Topologies: Casimir Energies
• Witten's 2+1 gravity on R x (Klein bottle)