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## Banach Center Publications

1997 | 39 | 1 | 303-315
Tytuł artykułu

### The Group of Large Diffeomorphisms in General Relativity

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate the mapping class groups of diffeomorphisms fixing a frame at a point for general classes of 3-manifolds. These groups form the equivalent to the groups of large gauge transformations in Yang-Mills theories. They are also isomorphic to the fundamental groups of the spaces of 3-metrics modulo diffeomorphisms, which are the analogues in General Relativity to gauge-orbit spaces in gauge theories.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
303-315
Opis fizyczny
Daty
wydano
1997
Twórcy
autor
• Fakultät für Physik der Universität Freiburg, Hermann Herder Straße 3, D-79104 Freiburg, Germany
Bibliografia
• [1] A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourão, and T. Thiemann, Quantization of diffeomorphism invariant theories with local degrees of freedom, J. Math. Phys. 36 (1995), 6456-6493; gr-qc/9504018.
• [2] H. S. M. Coxeter and W. O. J. Moser, Generators and relations for discrete groups (second edition), Springer Verlag, Berlin-Göttingen-Heidelberg-New York, 1965.
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• [4] J. Friedman and D. Witt, Homotopy is not isotopy for homeomorphisms of 3-manifolds, Topology 25 (1986), 35-44.
• [5] D. Giulini, Asymptotic symmetry groups of long-ranged gauge configurations, Modern Phys. Lett. A 10 (1995), 2059-2070.
• [6] D. Giulini, On the configuration space topology in general relativity, Helv. Phys. Acta 68 (1995), 87-111.
• [7] D. Giulini, Quantum mechanics on spaces with finite fundamental group, Helv. Phys. Acta 68 (1995), 438-469.
• [8] D. Giulini, What is the geometry of superspace?, Phys. Rev. D (3) 51 (1995), 5630-5635.
• [9] D. Giulini, 3-Manifolds for relativists, Internat. J. Theoret. Phys. 33 (1994), 913-930.
• [10] D. Giulini and J. Louko, Diffeomorphism invariant states in Wittens 2+1 quantum gravity on $R×T^2$, Classical Quantum Gravity 12 (1995), 2735-2745.
• [11] D. Giulini and J. Louko, Theta-sectors in spatially flat quantum cosmology, Phys. Rev. D (3) 46 (1992), 4355-4364.
• [12] A. Hatcher, Homeomorphisms of sufficiently large $P^2$-irreducible 3-manifolds, Topology 15 (1976), 343-347.
• [13] J. Hempel, 3-Manifolds, Ann. of Math. Stud. 86, Princeton University Press, 1976.
• [14] H. Hendriks, Application de la théorie d'obstruction en dimension 3, Bull. Soc. Math. France Mém. 53 (1977), 81-195.
• [15] H. Hendriks and D. McCullough, On the diffeomorphism group of a reducible 3-manifold, Topology Appl. 26 (1987), 25-31.
• [16] D. McCullough, Mappings of reducible manifolds, in: Geometric and Algebraic Topology, Banach Center Publ. 18 (1986), 61-76.
• [17] D. McCullough, Topological and algebraic automorphisms of 3-manifolds, in: Groups of Homotopy, Equivalences and Related Topics, R. Piccinini (ed.), Lecture Notes in Math. 1425, Springer, Berlin, 1990, 102-113.
• [18] D. McCullough and A. Miller, Homeomorphisms of 3-manifolds with compressible boundary, Mem. Amer. Math. Soc. 344 (1986).
• [19] J. Milnor, Introduction to algebraic K-theory, Ann. of Math. Stud. 72, Princeton University Press, 1971.
• [20] S. P. Plotnick, Equivariant intersection forms, knots in $S^4$, and rotations in 2-spheres, Trans. Amer. Math. Soc. 296 (1986), 543-575.
• [21] D. Witt, Symmetry groups of state vectors in canonical quantum gravity, J. Math. Phys. 27 (1986), 573-592.
• [22] D. Witt, Vacuum space-times that admit no maximal slice, Phys. Rev. Lett. 57 (1986), 1386-1389.
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Bibliografia
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