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The topology of the large-scale structure of the universe
Abstract
It has been suggested recently that the topology of a distribution of galaxies can be characterized by the mean Gaussian curvature per unit volume of surfaces of constant density. An expression is derived which relates the mean curvature of isodensity surfaces to the power spectrum of density fluctuations in the linear regime of Gaussian fluctuations with random phases. The result may be compared to real galaxy catalogs if the galaxy density is smoothed over scales larger than a correlation length. The implications of the result for understanding the large-scale structure of the universe are discussed.
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Gott et al. (1986) and Hamilton et al. (1986) considered the genus of the level surfaces as a useful numerical invariant of the cosmic web.
“Gott et al. (1986) and Hamilton et al. (1986) considered the genus of the level surfaces as a useful numerical invariant of this situation.”
From Topological pattern recognition for point cloud data (2014) · cites this paper as Hamilton et al. (1986)
The first recognition that topological methods could be useful in this setting occurred in Gott, Dickinson and Melott (1986) and Hamilton, Gott and Weinberg (1986).
“The first recognition that topological methods could be useful in this setting occurred in Gott, Dickinson and Melott (1986) and Hamilton, Gott and Weinberg (1986).”
From Topological pattern recognition for point cloud data (2014) · cites this paper as Hamilton et al. (1986)
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Cited by 123
Metadata
- Authors
- Hamilton, A. J. S., Gott, J. R., III, & Weinberg, D.
- Affiliations
- Princeton University (US)
- Venue
- The Astrophysical Journal
- Publisher
- American Astronomical Society
- Published
- 1986-10
- Volume
- 309
- Pages
- 1
- ISSN
- 0004-637X (ISSN-L)
- 1538-4357
- OpenAlex
- W1968018748
- Cited by
- 123
- References
- 0
- Citations by year
- 2025: 1 · 2024: 6 · 2023: 4 · 2022: 3 · 2021: 6 · 2020: 2 · 2019: 3 · 2018: 4 · 2017: 1 · 2016: 2 · 2015: 4 · 2014: 4 · 2013: 6 · 2012: 4
- FWCI
- 2.42
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- The Astrophysical Journal (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Keywords
- large-scale structure, galaxy distribution, topology, Gaussian curvature, isodensity surfaces, linear perturbation theory, random phase, galaxy catalog, correlation length
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