Les éléments d’homologie des quadriques et des hyperquadriques
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Pontryagin showed that the unitary and symplectic groups have no torsion, and all torsion elements of the orthogonal group have order two.
“Pontryagin has shown in his explicit construction [99] that the unitary and symplectic group have no torsion at all, and that all the torsion elements of the orthogonal group are of order two.”
From Topology of Lie groups (1952) · cites this paper as [99]
Section 3, “Groupes d’homologie,” discusses torsion in the homology of quadrics, not torsion in unitary, symplectic, or orthogonal groups. Searches for Pontryagin and for those groups’ torsion found no passage in our copy stating the attributed result. (LLM, conf=0.76)
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Samelson, H. (1952) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1952-09544-6 · Cited by 219 · see citing works
“Similar methods have been used to determine the homology invariants of the quadrics (real, complex, quaternion, hermitian) and similar spaces [32-37; 95; 118].”
Method
- Authors
- Nordon, J.
- Corresponding author
- Nordon, Jean
- Venue
- Bulletin de la Société mathématique de France
- Publisher
- Societe Mathematique de France
- Published
- 1946
- Volume
- 2
- Pages
- 116-129
- ISSN
- 0037-9484 (ISSN-L)
- 2102-622X
- OpenAlex
- W2583408678
- Semantic Scholar
- e1b04e92dc5889be9de8af99848bebe9ec87b526
- Cited by
- 7
- References
- 0
- FWCI
- 0.00
- Type
- journal article
- Language
- fr
- Open access
- bronze
- doi.org
- Locations
- Bulletin de la Société mathématique de France (publishedVersion)
- French digital mathematics library (Numdam) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic Geometry and Number Theory
- Physical Sciences › Mathematics › Geometry and Topology › Mathematics and Applications
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Algebra and Geometry
- Keywords
- homology, quadric surfaces, hyperquadrics, algebraic geometry, quadric hypersurfaces
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