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Parametrization of the Moduli Space of Flat SL(2, R) Connections on the Torus
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“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]
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Research works printed but not linked: 18
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- Guruprasad, K., Huebschmann, J, Jeffrey, L. and Weinstein, A.: Group systems, groupoids, and moduli spaces of parabolic bundles, Duke Math. J. 89(2) (1997), 377–412. · DOI
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- Hitchin, N. J.: The self-duality equations on a Riemann surface, Proc. London Math. Soc. 55(3) (1987), 59–126. · DOI
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- Nelson J. E., Regge T. and Zertuche F.: Homotopy groups and 2 + 1-dimensional quantum De Sitter gravity, Nuclear Phys. B 339 (1990), 516–532; Nelson, J. E. and Regge, T.: 2 + 1 quantum gravity, Phys. Lett. B 272 (1991), 213-216; Carlip, S. and Nelson, J. E.: Comparative quantizations of 2+1 gravity, Phys. Rev. D 51(10) (1995), 5643-5653. · DOI · Paper page
- Carlip, S.: Quantum gravity in 2 + 1 dimensions, Cambridge Monogr. Math. Phys., Cambridge Univ. Press, Cambridge, 1998. · DOI · Paper page
- Nelson, J. E. and Picken, R. F.: Quantum holonomies in (2 + 1)-dimensional gravity, Phys. Lett. B 471 (2000), 367–372. · DOI · Paper page
- Nelson, J. E. and Picken, R. F.: Quantum matrix pairs, Lett. Math. Phys. 52 (2000), 277–290. · DOI
- Caetano, A. and Picken, R. F.: An axiomatic definition of holonomy, Internat. J. Math. 5 (1994), 835–848. · DOI
- Barrett, J. W.: Holonomy and path structures in general relativity and Yang-Mills theory, Internat. J. Theoret. Phys. 30 (1991), 1171–1215. · DOI
- Ezawa, K.: Reduced phase space of the first order Einstein gravity on R x T 2, Osaka preprint OU-HET-185 (1993), hep-th/9312151; Chern-Simons quantization of (2 + 1) anti-de Sitter gravity on a torus, Classical Quantum Gravity 12 (1995), 373–392; Classical and quantum evolutions of the de Sitter and anti-de Sitter universes in (2 + 1) dimensions, Phys. Rev. D 49 (1994), 5211-5226, Addendum, ibid. D 50 (dy1995), 2935-2938. · DOI · Paper page
- deWit, B., Matschull, H.-J. and Nicolai, H.: Physical states in d = 3; N = 2 supergravity, Phys. Lett. B 318 (1993), 115–121. · DOI · Paper page
- Louko, J. and Marolf, D. M.: The solution space of 2 + 1 gravity on R x T 2 in Witten's connection formulation, Classical Quantum Gravity 11 (1994), 311–330. · DOI · Paper page
- Louko, J.: Witten's 2 + 1 gravity on Rx (Klein bottle), Classical Quantum Gravity 12 (1995), 2441–2467. · DOI
- Falceto, F. and Gawedzki, K.: Chern-Simons states at genus one, Comm. Math. Phys. 159 (1994), 549–579. · DOI
- Ashtekar, A. and Lewandowski, J.: Completeness of Wilson loop functionals on the moduli space of SL(2, C) and SU(1, 1) connections, Classical Quantum Gravity 10 (1993), L69–L74. · DOI
- Mikovic, A. and Picken, R. F.: Super Chern-Simons theory and flat super connections on a torus, math-ph/0008006, to appear in Adv. Theoret. Math. Phys. · arXiv
Cited by
Sorted by citations
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
Metadata
- 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 › Algebra and Number Theory › 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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