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Free subgroups in linear groups
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Given one projective structure there are infinitely many others with the same holonomy.
“and that given one projective structure there are infinitely many others with the same holonomy, but the map from the space of projective structures to the space of holonomy representations is not a covering map [47, 48].”
From Lorentz spacetimes of constant curvature (2007) · cites this paper as [48]
The passages on attracting and repulsing subspaces (§3.6) and the proof of Theorems 3 and 4 (§4.5; page numbers unavailable) concern projective transformations and linear groups, not projective structures. Searches for structures with the same holonomy and for the holonomy map found no passage addressing the claim. (LLM, conf=0.76)
Experimental — accuracy not yet measuredThe map from the space of projective structures to the space of holonomy representations is not a covering map.
“and that given one projective structure there are infinitely many others with the same holonomy, but the map from the space of projective structures to the space of holonomy representations is not a covering map [47, 48].”
From Lorentz spacetimes of constant curvature (2007) · cites this paper as [48]
The passages in §3.6 concern projective transformations and their attracting and repulsing subspaces; those in §4 concern linear groups. A search for projective structures, holonomy representations, and the covering-map claim found no passage addressing that map. (LLM, conf=0.76)
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Research works printed but not linked: 8
- Borel, 1965, Groupes réductifs, Publ. Math. I. H. E. S., 27, 55, 10.1007/BF02684375 · DOI
- Borel, 1971, Éléments unipotents et sous-groupes paraboliques de groupes réductifs, I, Invent. Math., 12, 95, 10.1007/BF01404653 · DOI
- Platonov, 1967, Lineinye gruppy s toždestvennymi sootnošenijami, Dokl. Akad. Nauk BSSR, 11, 581
- Platonov, 1969, O probleme Malčeva, Mat. Sbornik, 79, 621
- Tits, 1971, Représentations linéaires irréductibles d'un groupe réductif sur un corps quelconque, J. Reine Angew. Math., 247, 196
- Weil, 1967, Basic number theory, 10.1007/978-3-662-00046-5 · DOI
- Wolf, 1968, Growth of finitely generated solvable groups and curvature of Riemannian manifolds, J. Differential Geom., 2, 421, 10.4310/jdg/1214428658 · DOI
- Zassenhaus, 1969, On linear Noetherian groups, J. Number Theory, 1, 70, 10.1016/0022-314X(69)90026-2 · DOI
Cited by
Sorted by citations
Gromov, M. (1987) · Mathematical Sciences Research Institute Publications · doi:10.1007/978-1-4613-9586-7_3 · Cited by 1,817
Lorentz spacetimes of constant curvature
Mess, G. (2007) · Geometriae Dedicata · doi:10.1007/s10711-007-9155-7 · Cited by 278
Lorentz spacetimes of constant curvature
Mess, G. (2007) · arXiv · Cited by 5
Metadata
- Authors
- Tits, J.
- Affiliations
- University of Bonn (DE)
- Corresponding author
- Tits, J
- Venue
- Journal of Algebra
- Publisher
- Elsevier BV
- Published
- 1972-02
- Volume
- 20
- Issue
- 2
- Pages
- 250-270
- ISSN
- 0021-8693 (ISSN-L)
- OpenAlex
- W2040034546
- Cited by
- 825
- References
- 0
- Citations by year
- 2026: 13 · 2025: 23 · 2024: 16 · 2023: 34 · 2022: 14 · 2021: 24 · 2020: 23 · 2019: 40 · 2018: 29 · 2017: 26 · 2016: 32 · 2015: 19 · 2014: 27 · 2013: 30 · 2012: 31
- FWCI
- 6.17
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Journal of Algebra (publishedVersion)
- Dépôt institutionnel de l'Université libre de Bruxelles (Université Libre de Bruxelles) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Finite Group Theory Research
- Physical Sciences › Mathematics › Algebra and Number Theory › Advanced Algebra and Geometry
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Keywords
- free subgroups, linear groups, free groups, algebraic groups
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