Topology change in (2+1)-dimensional gravity
Open accessAbstract
In (2+1)-dimensional general relativity, the path integral for a manifold M can be expressed in terms of a topological invariant, the Ray–Singer torsion of a flat bundle over M. For some manifolds, this makes an explicit computation of transition amplitudes possible. In this paper, the amplitude for a simple topology-changing process is evaluated. It is shown that certain amplitudes for spatial topology change are nonvanishing—in fact, they can be infrared divergent—but that they are infinitely suppressed relative to similar topology-preserving amplitudes.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Carlip and Cosgrove explicitly compute amplitudes for a transition between a genus three surface and a pair of genus two surfaces.
“Carlip and Cosgrove [84], for example, explicitly compute amplitudes for a transition between a genus three surface and a pair of genus two surfaces.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [84]
For manifolds with boundary, the path integral gives a transition function depending on specified boundary data, most simply the induced spin connection ω, with restrictions on the normal component of ω and the triad E.
“The path integral then gives a transition function that depends on specified boundary data — most simply, the induced spin connection ω, with some additional restrictions on the normal component of ω and the triad E [283, 84].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [84]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
2 + 1 dimensional gravity as an exactly soluble system
Witten, E. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90143-5 · Cited by 2,562 · see citing works
Flagged first, then by citations
Research works printed but not linked: 3
- [7][7] S. Carlip, "Six Ways to Quantize (2+1)-Dimensional Gravity," to appear in Proc. of the Fifth Canadian Conference on General Relativity and Relativistic Astrophysics, Waterloo, Ontario, May 1993.
- [24][24] See, for example, W. Abikoff, The Real Analytic Theory of Teichmüller Space (Springer, 1976).
- [25][25] C. R. F. Maunder, Algebraic Topology (Cambridge University Press, 1980).
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 · see citing works
Self-citationBarrett, J. W., & Naish-Guzman, I. (2009) · Classical and Quantum Gravity · doi:10.1088/0264-9381/26/15/155014 · Cited by 131 · see citing works
Carlip, S. (2023) · Reports on Progress in Physics · doi:10.1088/1361-6633/acceb4 · Cited by 41 · see citing works
Self-citation
- Authors
- Carlip, S., & Cosgrove, R.
- Affiliations
- University of California, Davis (US)
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1994-10-01
- Volume
- 35
- Issue
- 10
- Pages
- 5477-5493
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2079646839
- Cited by
- 26
- References
- 1
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 1 · 2023: 1 · 2021: 2 · 2016: 1 · 2015: 1 · 2012: 1
- FWCI
- 1.07
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Mathematical Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- U.S. Department of Energy (FG0391ER40674)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- three-dimensional gravity, topology change, Ray-Singer torsion, flat bundles, path integral, transition amplitudes, infrared divergences, topological invariants, quantum gravity
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
