1992/01/30 by K. Amano, Kaoru Amano, Saburo Higuchi +1 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.1016/0550-3213(92)90022-4
published as Nucl.Phys. B377 (1992) 218-235 · 24 pages and 4 figures (not included)
arxiv created 1992/01/30 · openalex publication_date 1992/06/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In 2+1 dimensional gravity, a dreibein and the compatible spin connection can represent a space-time containing a closed spacelike surface Σ only if the associated SO(2,1) bundle restricted to Σ has the same non-triviality (Euler class) as that of the tangent bundle of Σ. 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 ≥ 2 spaces.