Armand Borel (21 May 1923 –11 August 2003) was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993. He worked in algebraic topology, in the theory of Lie groups, and was one of the creators of the contemporary theory of linear algebraic groups. May 21 is the 141st day of the year (142nd in leap years) in the Gregorian calendar. ... Year 1923 (MCMXXIII) was a common year starting on Monday (link will display the full calendar) of the Gregorian calendar. ... is the 223rd day of the year (224th in leap years) in the Gregorian calendar. ... Year 2003 (MMIII) was a common year starting on Wednesday (link displays 2003 calendar) of the Gregorian calendar. ... Leonhard Euler, one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... Location within Switzerland La Chaux-de-Fonds is a city located in the Jura mountains in Switzerland. ... Fuld Hall The Institute for Advanced Study is a private institution in Princeton Township, New Jersey, U.S.A., designed to foster pure cutting-edge research by scientists and scholars in a variety of fields without the complications of teaching or funding, or the agendas of sponsorship. ... Nassau Street, Princetons main street. ... Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. ... In mathematics, a Lie group, named after Norwegian mathematician Sophus Lie (IPA pronunciation: , sounds like Lee), is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. ... In mathematics, a linear algebraic group is a subgroup of the group of invertible n×n matrices (under matrix multiplication) that is defined by polynomial equations. ...

He studied at the ETH Zürich. He came under the influence of the topologist Heinz Hopf, and the Lie group theorist Eduard Stiefel. He was in Paris from 1949: he applied the Leray spectral sequence to the topology of Lie groups and their classifying spaces, under the influence of Jean Leray and Henri Cartan. ETH Zurich (from its German name Eidgenössische Technische Hochschule Zürich, ETHZ) is the Swiss Federal Institute of Technology in Zürich, Switzerland. ... Heinz Hopf (November 19, 1894 – June 3, 1971) was a mathematician born in Gräbschen, Germany. ... Eduard L. Stiefel (21 April 1909 – 25 November 1978) was a mathematician. ... In homological algebra, especially in algebraic topology or group cohomology, a spectral sequence is a means of computing homology groups by taking successive approximations. ... In mathematics, a classifying space in homotopy theory of a discrete group G is, roughly speaking, a path connected topological space X such that the fundamental group of X is isomorphic to G and the higher homotopy groups of X are trivial. ... Jean Leray (7 November 1906-10 November 1998) was a French mathematician, who worked on both partial differential equations and algebraic topology. ... Henri Cartan (born July 8, 1904) is a son of Élie Cartan, and is, as his father was, a distinguished and influential French mathematician. ...

He collaborated with Jacques Tits in fundamental work on algebraic groups, and with Harish-Chandra on their arithmetic subgroups. In an algebraic group G a Borel subgroup H is one such that the homogeneous space G/H is a projective 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 various flag manifolds). Both those aspects generalize, and play a central role in the theory. Jacques Tits (born August 12, 1930) is a French mathematician, formerly Belgian. ... In algebraic geometry, an algebraic group is a group that is an algebraic variety, such that the multiplication and inverse are given by regular functions on the variety. ... See Harishchandra for the character in Hindu mythology Harish-Chandra (11 October 1923-16 October 1983) was an Indian mathematician, who did fundamental work in representation theory. ... In mathematics, an arithmetic group (arithmetic subgroup) in a linear algebraic group G defined over a number field K is a subgroup Γ of G(K) that is commensurable with G(O), where O is the ring of integers of K. Here two subgroups A and B of a group... In mathematics, in particular in the theory of Lie groups, algebraic groups and topological groups, a homogeneous space for a group G is a manifold or topological space X on which G acts by symmetry in a transitive way; it is not assumed that the action of G is faithful. ... This article is about algebraic varieties. ... In the history of mathematics, the origins of group theory lie in the search for a proof of the general unsolvability of quintic and higher equations, finally realized by Galois theory. ... In mathematics, a Borel subgroup (named after Armand Borel) of an algebraic group G is a maximal solvable subgroup. ... In mathematics, a flag manifold (or flag variety) is the set of all flags in a finite-dimensional vector space V. The flag variety on V is naturally a projective variety. ...

The Borel-Moore homology theory applies to general locally compact spaces, and is closely related to sheaf theory. In mathematics, Borel-Moore homology or homology with closed support is a homology theory for locally compact spaces. ... In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space. ... In mathematics, a sheaf F on a topological space X is something that assigns a structure F(U) (such as a set, group, or ring) to each open set U of X. The structures F(U) are compatible with the operations of restricting the open set to smaller subsets and...

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.) Félix Édouard Justin Émile Borel (January 7, 1871 – February 3, 1956) was a French mathematician and politician. ...

External links

• "Armand Borel" - obituary on Institute for Advanced Study website
• "Armand Borel (1923-2003)" - obituary in Notices of the AMS.
• O'Connor, John J; Edmund F. Robertson "Armand Borel". MacTutor History of Mathematics archive.