Quantum general relativity and the classification of smooth manifolds

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dc.creatorPfeiffer, Hendryk
dc.date2004-04-21
dc.date2004-05-17
dc.date.accessioned2026-07-07T03:28:37Z
dc.date.available2026-07-07T03:28:37Z
dc.descriptionThe gauge symmetry of classical general relativity under space-time diffeomorphisms implies that any path integral quantization which can be interpreted as a sum over space-time geometries, gives rise to a formal invariant of smooth manifolds. This is an opportunity to review results on the classification of smooth, piecewise-linear and topological manifolds. It turns out that differential topology distinguishes the space-time dimension d=3+1 from any other lower or higher dimension and relates the sought-after path integral quantization of general relativity in d=3+1 with an open problem in topology, namely to construct non-trivial invariants of smooth manifolds using their piecewise-linear structure. In any dimension d<=5+1, the classification results provide us with triangulations of space-time which are not merely approximations nor introduce any physical cut-off, but which rather capture the full information about smooth manifolds up to diffeomorphism. Conditions on refinements of these triangulations reveal what replaces block-spin renormalization group transformations in theories with dynamical geometry. The classification results finally suggest that it is space-time dimension rather than absence of gravitons that renders pure gravity in d=2+1 a `topological' theory.
dc.description41 pages, LaTeX2e with combined eps/PicTeX figures; v2: inaccuracies fixed
dc.identifierhttps://arxiv.org/abs/gr-qc/0404088
dc.identifierhttp://arxiv.org/abs/gr-qc/0404088
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/34901
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.titleQuantum general relativity and the classification of smooth manifolds
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