Armand Borel's mathematical work centered on the theory of Lie groups.
Because of the increasingly important place of this theory in the whole
of mathematics, Borel's work influenced some of the most important
developments of contemporary mathematics. His first great achievement
was to apply to Lie groups and homogenous spaces the powerful techniques
of algebraic topology developed by Leray, Cartan and Steenrod. In 1992,
Borel was awarded the International Balzan Prize for Mathematics "for
his fundamental contributions to the theory of Lie groups, algebraic
groups and arithmetic groups, and for his indefatigable action in favor
of high quality in mathematical research and of the propagation of new
ideas." He wrote more than 145 articles before 1982, which were
collected in three volumes published in 1983. A fourth volume of
subsequent articles was published in 2001. Volume II collects the papers
written from 1959 to 1968.