USS Amsterdam

See also: Borel

Armand Borel (May 21st 1923 with La Chaux-de-Fonds - August 11th 2003 with Princeton) was a Swiss Mathématicien and permanent professor with the Institute for Advanced Study, Princeton, of 1957 with 1993. He worked in algebraic Topologie, in the theory of the groups of Dregs, and was one of the creators of the modern theory of the algebraic linear groups.

He made his studies with the ETH Zurich. He was subject to the influence of the topologist Heinz Hopf, and of the specialist in the groups of Dregs Stiefel. In Paris starting from 1949, it applied the spectral continuation of Leray to the topology of the groups of Dregs and their classifying spaces, under the influence of Jean Leray and Henri Cartan.

He collaborated with Jacques Tits on a fundamental work on the algebraic groups, and with Harish-Chandra on theirs under arithmetic groups. In an algebraic group, a sub-group of Borel (or very short Borel ) is a sub-group B such as homogeneous space G/B is a projective and minimal variety for this property. For example, if G is GL_n then one can take for B the sub-group of the higher triangular matrices. In this case, B is a resolvable sub-group maximum and the parabolic sub-groups P ranging between B and G have a combinative structure (here, varieties G/P are varieties of flags). All these objects spread and play a central role in the theory.

The theory of the homology of Borel-Moore applies to the spaces locally compact and is close to the theory of the beams.

It published many books, including one on the history of the theory of the groups of Dregs.

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