Parametrization of the Moduli Space of Flat SL(2, R) Connections on the Torus
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Only the hyperbolic-hyperbolic sector corresponds to a spacetime in which the T2 slices are spacelike.
“It may be shown that only the hyperbolic-hyperbolic sector corresponds to a spacetime in which the T2 slices are spacelike [117, 119, 182, 209].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [209]
Section 2 (p. 3) classifies the connection matrices, and the Discussion (pp. 8–9) describes the resulting sectors. Neither those passages nor searches for spacelike torus slices and spacetime address which sector permits spacelike T² slices. (LLM, conf=0.75)
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Research works printed but not linked: 5
- [1][1] Atiyah, M. F.; Bott, R.,'The Yang-Mills equations over Riemann surfaces,' Philos. Trans. Roy. Soc. London Ser. A 308, 523-615 (1983). -
- [4][4] Hitchin, N. J., 'The self-duality equations on a Riemann surface,' Proc. London Math. Soc. 55 (3), 59-126 (1987) -
- [7][7] Carlip, S., 'Quantum gravity in 2 + 1 dimensions,' Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge (1998). -
- [12][12] Ezawa K., 'Reduced Phase Space of the First Order Einstein Gravity on R × T 2 ,' Osaka preprint OU-HET-185 (1993),hep-th/9312151; 'Chern-Simons quantization of (2+1) anti-de Sitter gravity on a torus,' Class. Quant. Grav. 12, 373-392 (1995); 'Classical and quantum evolutions of the de Sitter and anti-de Sitter universes in (2+1) dimensions,' Phys. Rev. D49, 5211-5226 (1994), Addendum-ibid D50, 2935-2938 (1995). - · arXiv
- [18][18] Mikovic, A.; Picken, R. F., 'Super Chern-Simons theory and flat super connections on a torus,' math-ph/0008006, to appear in Adv. Theor. Math. Phys. µ Figure 1: Subspace of A or B pairs <!-- image --> Figure 2: Subspace of B or C pairs <!-- image --> Figure 3: Subspace of B or D pairs <!-- image --> Figure 4: Overall view of the moduli space <!-- image --> · arXiv
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Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe
Carlip, S. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-1 · Cited by 172 · see citing works
- Authors
- Nelson, J. E., & Picken, R. F.
- Affiliations
- Istituto Nazionale di Fisica Nucleare, Sezione di Torino (IT)
- Instituto Superior Técnico (PT)
- Venue
- Letters in Mathematical Physics
- Published
- 2002-03
- Volume
- 59
- Issue
- 3
- Pages
- 215-226
- ISSN
- 0377-9017 (ISSN-L)
- 1573-0530
- OpenAlex
- W1487445280
- Cited by
- 6
- References
- 0
- FWCI
- 1.59
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Letters in Mathematical Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Institutional Research Information System University of Turin (University of Turin) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Istituto Nazionale di Fisica Nucleare
- Ministero dell'Università e della Ricerca
- Fundação para a Ciência e a Tecnologia
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Algebra and Geometry
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic structures and combinatorial models
- Keywords
- moduli spaces, flat connections, SL(2,R), torus, gauge equivalence, commuting matrices, simultaneous conjugation, canonical form, spectral properties, Hausdorff topology
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