2006/06/29 by Domenico Giulini, Giulini, Domenico
Mathematics · Physics and Astronomy · #57N10 #83C45 #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th #math-ph #math.MP #msc:57N10 #msc:83C45
paper · pdf · doi:10.48550/arxiv.math-ph/0606066
41 pages, 8 figures (colored)
arxiv created 2006/06/29 · openalex publication_date 2006/06/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Mapping-class groups of 3-manifolds feature as symmetry groups in canonical quantum gravity. They are an obvious source through which topological information could be transmitted into the quantum theory. If treated as gauge symmetries, their inequivalent unitary irreducible representations should give rise to a complex superselection structure. This highlights certain aspects of spatial diffeomorphism invariance that to some degree seem physically meaningful and which persist in all approaches based on smooth 3-manifolds, like geometrodynamics and loop quantum gravity. We also attempt to give a flavor of the mathematical ideas involved.