Troels Jørgensen

Troels Jørgensen is a Danish mathematician at Columbia University working on hyperbolic geometry and complex analysis, who proved Jørgensen's inequality. He wrote his thesis in 1970 at the University of Copenhagen under the joint supervision of Werner Fenchel and Bent Fuglede.^[1]

He is known for Jørgensen's inequality,^[2] and for his discovery of a hyperbolic structure on certain fibered 3-manifolds^[3] which were one of the inspirations for William Thurston's Geometrisation Conjecture.^[4] He is also credited with being one of the co-discoverers of the ordered structure of the set of volumes of hyperbolic 3-manifolds.^[5]^[6]

[1]
Troels Jørgensen at the Mathematics Genealogy Project
[2]
Jørgensen, Troels (1976), "On discrete groups of Möbius transformations", American Journal of Mathematics, 98 (3): 739–749, doi:10.2307/2373814, ISSN 0002-9327, JSTOR 2373814, MR 0427627
[3]
Jørgensen, Troels (1977). "Compact 3-manifolds of constant negative curvature fibering over the circle". Ann. Math. (2). 106: 61–72. Zbl 0368.53025.
[4]
Thurston, William P. (1982), "Three-dimensional manifolds, Kleinian groups and hyperbolic geometry", Bulletin of the American Mathematical Society, New Series, 6 (3): 357–381, doi:10.1090/S0273-0979-1982-15003-0, ISSN 0002-9904, MR 0648524, p. 362
[5]
Thurston, loc. cit., Theorem 3.5 on p. 364
[6]
Gromov, Michael (1981), "Hyperbolic manifolds according to Thurston and Jorgensen", Semin. Bourbaki, 32e annee, Vol. 1979/80, Lect. Notes Math., Signature Books, pp. 40–53, Zbl 0452.51017

Work