- Armand Borel
Armand Borel (
21 May 1923 –11 August 2003 ) was a Swissmathematician , born inLa Chaux-de-Fonds , and was a permanent professor at theInstitute for Advanced Study inPrinceton, New Jersey ,United States from 1957 to 1993. He worked inalgebraic topology , in the theory ofLie group s, and was one of the creators of the contemporary theory oflinear algebraic group s.He studied at the
ETH Zürich . He came under the influence of the topologistHeinz Hopf , and the Lie group theoristEduard Stiefel . He was in Paris from 1949: he applied the Lerayspectral sequence to the topology of Lie groups and theirclassifying space s, under the influence ofJean Leray andHenri Cartan .He collaborated with
Jacques Tits in fundamental work onalgebraic group s, and withHarish-Chandra on their arithmetic subgroups. In an algebraic group "G" a "Borel subgroup" "H" is one such that thehomogeneous space "G/H" is aprojective variety , and as small as possible. For example if "G" is GL"n" then we can take "H" to be the subgroup of upper triangular matrices. In this case it turns out that H is a maximal solvable subgroup, and that the parabolic subgroups "P" between "H" and "G" have a combinatorial structure (in this case the homogenous spaces "G/P" are the variousflag manifold s). Both those aspects generalize, and play a central role in the theory.The
Borel-Moore homology theory applies to generallocally compact space s, and is closely related to sheaf theory.He published a number of books, including work on the history of Lie groups.
He died in Princeton. (He used to answer the question of whether he was related to
Émile Borel alternately by saying he was a nephew, and no relation.)ee also
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Borel–Bott–Weil theorem External links
* [http://www.ias.edu/Newsroom/announcements/Uploads/view.php?cmd=view&id=19 "Armand Borel"] - obituary on Institute for Advanced Study website
* [http://www.ams.org/notices/200405/fea-borel.pdf "Armand Borel (1923-2003)"] - obituary in Notices of the AMS.
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