Abstract
In canonical quantum gravity certain topological properties of 3-manifolds are of interest. This article gives an account of those properties which have so far received sufficient attention, especially those concerning the diffeomorphism groups of 3-manifolds. We give a summary of these properties and list some old and new results concerning them. The appendix contains a discussion of the group of large diffeomorphisms of thel-handle 3-manifold.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aneziris, C., Balachandran, A. P., Bourdeau, M., Jo, S., Ramadas, T. R., and Sorkin, R. (1989),International Journal of Modern Physics A,4, 5459–5510.
Coxeter, H. S. M. and Moser, W. O. J. (1965).Generators and Relations for Discrete Groups, 2nd edition, Springer-Verlag, Berlin, Göttingen, Heidelberg, New York.
Friedman, J., and Sorkin, R. (1980).Physical Review Letters,44, 1100–1103.
Gibbons, G. W., and Hawking, S. W. (1992).Communications in Mathematical Physics,148, 345–352.
Giulini, D. (1992a). On the configuration space topology in general relativity, Preprint, Freiburg THEP-92/32 and gr-qc 9301020, submitted for publication.
Giulini, D. (1992b).Communications in Mathematical Physics 148, 353–357.
Giulini, D. (1993). Quantum mechanics on spaces with finite non-Abelian fundamental group, in preparation.
Giulini, D., and Louko, J. (1992).Physical Review D,46, 4355–4364.
Gromov, M., and Lawson, B. (1983).Institut des Hautes Études Scientifique Publicationes Mathematiques,58, 294–408.
Hartle, J., and Witt, D. (1988).Physical Review D,37, 2833–2836.
Hempel, J. (1976).3-Manifolds, Princeton University Press, Princeton, New Jersey.
Hendriks, H., and Laudenbach, F. (1984).Topology,23, 423–443.
Hendriks, H., and McCullough, D. (1987).Topology and its Application,26, 25–31.
Isham, C. J. (1981).Physics Utters B,106, 188–192.
Laudenbach, F. (1974).Asterisque,12, 1–137.
Lee, K. B., Shin, J., and Yokura, S. (1993). Free actions of finite Abelian groups on the 3-torus, University of Oklahoma preprint.
McCullough, D. (1986).Geometric and Algebraic Topology (Warsaw),18, 61–76.
Milnor, J. (1971).Introduction to Algebraic K-Theory. Princeton University Press, Princeton, New Jersey.
Orlik, P. (1972).Seifert Manifolds, Springer-Verlag, Berlin.
Rourke, C., and de Sá, C. (1979).Bulletin of the American Mathematical Society, (New Series)1, 251–254.
Sorkin, R. (1989). Classical topology and quantum phases: Quantum geons, inGeometrical and Algebraic Aspects of Nonlinear Field Theory, S. De Filippo, M. Marinaro, G. Marmo, and G. Vilasi, eds., Elsevier, North-Holland.
Thomas, C. B. (1986).Elliptic Structures on 3-Manifolds, Cambridge University Press, Cambridge.
Thomas, C. B. (1988).Bulletin of the London Mathematical Society,20, 65–67.
Witt, D. (1986).Journal of Mathematical Physics,27, 573–592.
Witt, D. (1987). Topological obstructions to maximal slices, Santa Barbara preprint, UCSB-1987.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Giulini, D. 3-Manifolds for relativists. Int J Theor Phys 33, 913–930 (1994). https://doi.org/10.1007/BF00672824
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00672824