The DOI matches its Crossref record; 33 of the 33 references it cites were found in a registry or an index.
Right-angled Coxeter polytopes, hyperbolic six-manifolds, and a problem of Siegel
Abstract
By gluing together the sides of eight copies of an all-right angled hyperbolic six-dimensional polytope, two orientable hyperbolic six-manifolds with Euler characteristic −1 are constructed. They are the first known examples of orientable hyperbolic six-manifolds having the smallest possible volume.
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“There is ample evidence that different sectors of the landscape are connected, via known transitions changing topology [104][105][106][107][108], chirality [109], and even effective dimensionality [110][111][112][113], with dualities such as [114,115] relating curvature and dimensionality via the effective central charge.”
From Hyperbolic compactification of M-theory and de Sitter quantum gravity (2022) · cites this paper as [105]
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Serre, J.-P. (1973) · Graduate Texts in Mathematics · doi:10.1007/978-1-4684-9884-4 · Cited by 1,715
Foundations of Hyperbolic Manifolds
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Uber Die Analytische Theorie Der Quadratischen Formen III
Siegel, C. L. (1937) · The Annals of Mathematics · doi:10.2307/1968520 · Cited by 436
Minimum volume cusped hyperbolic three-manifolds
Gabai, D., Meyerhoff, R., & Milley, P. (2009) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-09-00639-0 · Cited by 124
DISCRETE GROUPS GENERATED BY REFLECTIONS IN LOBAČEVSKIĬ SPACES
Vinberg, E. B. (1967) · Mathematics of the USSR-Sbornik · doi:10.1070/sm1967v001n03abeh001992 · Cited by 112
The orientable cusped hyperbolic 3-manifolds of minimum volume
Cao, C., & Meyerhoff, G. R. (2001) · Inventiones mathematicae · doi:10.1007/s002220100167 · Cited by 106
On right-angled reflection groups in hyperbolic spaces
Potyagailo, L., & Vinberg, E. B. (2005) · Commentarii Mathematici Helvetici · doi:10.4171/cmh/4 · Cited by 66
Research works printed but not linked: 6
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- Löbell F.: Beispiele geschlossener dreidimensionaler Clifford-Kleinscher Räume negative Krümmung Ber. Verh. Sächs. Akad. Wiss. Leipzig, Math-Phys. Kl. 83, 167–174 (1931)
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Cited by
Hyperbolic compactification of M-theory and de Sitter quantum gravity
De Luca, G. B., Silverstein, E., & Torroba, G. (2022) · SciPost Physics · doi:10.21468/scipostphys.12.3.083 · Cited by 39
Metadata
- Authors
- Everitt, B., Ratcliffe, J. G., & Tschantz, S. T.
- Venue
- Mathematische Annalen
- Published
- 2011-11-17
- Volume
- 354
- Issue
- 3
- Pages
- 871-905
- ISSN
- 0025-5831
- 1432-1807
- Cited by
- 17
- References
- 33
- Language
- en
- Licence
- www.springer.com/tdm (tdm)
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- Everitt, B., Ratcliffe, J. G., & Tschantz, S. T. (2012). Right-angled Coxeter polytopes, hyperbolic six-manifolds, and a problem of Siegel. Mathematische Annalen. https://doi.org/10.1007/s00208-011-0744-2
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
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.
