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Self-duality in four-dimensional Riemannian geometry
Abstract
We present a self-contained account of the ideas of R. Penrose connecting four-dimensional Riemannian geometry with three-dimensional complex analysis. In particular we apply this to the self-dual Yang-Mills equations in Euclidean 4-space and compute the number of moduli for any compact gauge group. Results previously announced are treated with full detail and extended in a number of directions.
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Cites
An application of the Morse theory to the topology of Lie-groups
Bott, R. (1956) · Bulletin de la Société mathématique de France · doi:10.24033/bsmf.1472 · Cited by 280
Cited by
Topological quantum field theory
Witten, E. (1988) · Communications in Mathematical Physics · doi:10.1007/bf01223371 · Cited by 2,396
An application of gauge theory to four-dimensional topology
Donaldson, S. K. (1983) · Journal of Differential Geometry · doi:10.4310/jdg/1214437665 · Cited by 819
Irrationality and the $h$-cobordism conjecture
Donaldson, S. K. (1987) · Journal of Differential Geometry · doi:10.4310/jdg/1214441179 · Cited by 271
Chern numbers, quaternions, and Berry's phases in Fermi systems
Avron, J. E., Sadun, L., Segert, J., & Simon, B. (1989) · Communications in Mathematical Physics · doi:10.1007/bf01218452 · Cited by 129
Topological Invariants in Fermi Systems with Time-Reversal Invariance
Avron, J. E., Sadun, L., Segert, J., & Simon, B. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.1329 · Cited by 113
Metadata
- Authors
- Atiyah, M. F., Hitchin, N. J., & Singer, I. M.
- Venue
- Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- Publisher
- The Royal Society
- Published
- 1978-09-12
- Volume
- 362
- Issue
- 1711
- Pages
- 425-461
- ISSN
- 0080-4630 (ISSN-L)
- 2053-9169
- OpenAlex
- W2032317001
- Cited by
- 1,428
- References
- 1
- FWCI
- 30.24
- Type
- journal article
- Language
- en
- Open access
- closed
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- Atiyah, M. F., Hitchin, N. J., & Singer, I. M. (1978). Self-duality in four-dimensional Riemannian geometry. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences. https://doi.org/10.1098/rspa.1978.0143
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
